Set Week 3: Chapters 3 & 4 Chapter 3: Complete the EVEN numbers problems listed below; the problem set begins on page 100 in Gravetter and Wallnau (2013). The answers to the odd numbered problems are in the back of the book for additional practice. Provide the answer to each question number listed below using complete sentences in APA format. Steps completed to determine the answer may also be included. 2.) 4.) 6.) 14.) 18.) Additional Item: 1. Return to the four types of measurement scales (i.e., nominal, ordinal, interval and ratio) in Chapter 1 of Gravetter and Wallnau (2013). For each measurement scale select the most appropriated measures of central tendency. Also, for each measurement scale, identify any inappropriate measures of central tendency. Briefly explain your selections. Chapter 4: Complete the EVEN numbers problems listed below; the problem set begins on page 130 in Gravetter and Wallnau (2013). The answers to the odd numbered problems are in the back of the book for additional practice. Provide the answer to each question number listed below using complete sentences in APA format. Steps completed to determine the answer may also be included. 4.) 6.) For Items 16 and 18, please show the steps taken (show your work): 16.) 18.) 20.) 22.) Additional Items: 1. Every population has a parametric mean () and parametric standard deviation (). Briefly discuss the impact of sample size on these parametric values. 2. Fact: by increasing sample size, the researcher does not reduce the size of the parametric standard deviation () but does decrease the uncertainty associated with the estimation of parametric values. Briefly explain the implications of this fact. 3. The concept of Degrees of Freedom re-appears throughout the study of statistics. Given a sample size of five (n=5), what are the degrees of freedom? Provide a detailed example using real numbers. Problem Set Week 3: Chapters 3 & 4 Chapter 3: Complete the EVEN numbers problems listed below; the problem set begins on page 100 in Gravetter and Wallnau (2013). The answers to the odd numbered problems are in the back of the book for additional practice. Provide the answer to each question number listed below using complete sentences in APA format. Steps completed to determine the answer may also be included. 2.) 4.) 6.) 14.) 18.) Additional Item: 1. Return to the four types of measurement scales (i.e., nominal, ordinal, interval and ratio) in Chapter 1 of Gravetter and Wallnau (2013). For each measurement scale select the most appropriated measures of central tendency. Also, for each measurement scale, identify any inappropriate measures of central tendency. Briefly explain your selections. Chapter 4: Complete the EVEN numbers problems listed below; the problem set begins on page 130 in Gravetter and Wallnau (2013). The answers to the odd numbered problems are in the back of the book for additional practice. Provide the answer to each question number listed below using complete sentences in APA format. Steps completed to determine the answer may also be included. 4.) 6.) For Items 16 and 18, please show the steps taken (show your work): 16.) 18.) 20.) 22.) Additional Items: 1. Every population has a parametric mean () and parametric standard deviation (). Briefly discuss the impact of sample size on these parametric values. 2. Fact: by increasing sample size, the researcher does not reduce the size of the parametric standard deviation () but does decrease the uncertainty associated with the estimation of parametric values. Briefly explain the implications of this fact. 3. The concept of Degrees of Freedom re-appears throughout the study of statistics. Given a sample size of five (n=5), what are the degrees of freedom? Provide a detailed example using real numbers. SPSS Week 3 Imagine a researcher is interested in examining the psychological impact of principals' perceived conflict management style on teachers' productivity. In this case, the researcher is interested in the relationships among teachers' self-esteem, how teachers perceive their principals' conflict management style, and teachers' productivity in a convenience sample of 40 teachers. These teachers completed a survey including a number of demographic questions as well as measures to assess perceived principals' conflict management style, teacher's self-esteem, and productivity. Below are the demographic questions and participants' responses. Please use these data to complete the questions below (these data have already been entered in a SPSS file; see the note below the data table). What is your gender (M = male, F = female)? What is your age (in years)? How long have you been teaching (in years)? M M F M F F F F M M F F F F M M F M F M M M 52 35 45 47 62 29 50 43 54 40 44 53 56 28 51 30 45 36 57 58 59 34 25 14 10 20 30 2 23 13 29 19 22 5 16 11 15 2 15 11 18 10 21 5 What topic do you teach (M = math, S = science, A = art, FL = foreign language)? M M A S S A FL A S S S M M S S FL A M S S A S How many students are in your class? 18 23 27 21 21 29 25 31 24 25 32 30 19 28 21 22 27 29 30 20 27 23 F F M F M M F M F F F M F F M M F F 48 50 57 48 39 36 29 52 68 45 56 40 33 47 58 49 39 42 18 21 17 15 18 12 8 3 33 16 29 19 4 17 30 20 11 14 S M FL FL S M A A S A FL M M S A FL M FL 33 19 15 21 24 26 23 24 28 25 26 20 23 27 25 27 30 22 Download the SPSS data set: teachersurvey.sav. Not all of the variables in that SPSS file will be used for this assignment. Part of the goal of this activity is to explore the various tools under the ANALYZE tab in SPSS, the more exploring the more comfortable it will become. In this SPSS assignment, use the tools presented in Gravetter and Wallnau (2013) Chapters 3 and 4 to describe the central tendency and variability of the scores. The following video may also be helpful: https://www.youtube.com/watch?v=l5dDl_C3xCU 1. Split the file by gender. Calculate the mean and standard deviation of age and number of years teaching (experience) for males and females. Hint: use Explore found under the ANALSYS => Descriptives tabs. Age and Experience will be the dependent variable and Gender will be the factor. 2. Compute the mean, median, and mode for number of students in the class (class size). What value is the most representative measure of the central tendency for this variable and why? 3. Calculate the range of number of years teaching (experience). What does this information indicate about the years of experience? What does it indicate about the years of experience? 4. Using the data for age, change one score to 22. Please identify the score chosen to change. Calculate the new mean for the variable. Explain how and why the mean changed and the standard deviation of age. Note: before the data set (teachersurvey.sav) is saved, be sure to change the age back to its original number. 5. Create a frequency distribution graph for topics taught. What is the most appropriate measure of central tendency? Report this value (the appropriate measure of central tendency for this variable). What is the appropriated graphical representation of the frequency distribution? Generate with SPSS the graphical representation selected combined with supported answers. $FL2@(#) IBM SPSS STATISTICS MS Windows 24.0.0.0 ################(#########Y@26 Nov 1602:45:09 ###########################IDENTIFI########################GENDER ####1=male, 2=female########################AGE ########################EXPERIEN########################TOPIC ) ###1=math,2=science,3=art,4=foreign language ########################CLASSSIZ########################SCOREONE################ ########SCORETWO########################PRODONE ########################CONFLICT#################### #############################################################  ########################################################################## ################################################################## ##########IDENTIFI=Identifier GENDER=Gender AGE=Age EXPERIEN=Experience TOPIC=Topic CLASSSIZ=ClassSize SCOREONE=ScoreOne SCORETWO=ScoreTwo PRODONE=ProdOne CONFLICT=Conflict########################(######################Identifier: $@Role('0' )/Gender:$@Role('0' )/Age:$@Role('0' )/Experience:$@Role('0' )/Topic:$@Role('0' )/ClassSize:$@Role('0' )/ScoreOne:$@Role('0' )/ScoreTwo:$@Role('0' )/ProdOne:$@Role('0' )/Conflict:$@Role('0' )################UTF-8############,##########ee}ev}fereCom petitive {gfCompetitive ngCooperathexfyive ifCompetitive fyjCompetitive ffgkf{h}Cooperative lfCooperative qgCooperative mef|znewfCompetitive } ofCooperative zfCooperatpfieive qftCompetitive ewrCooperative fofsesfyCompetive teCooperative fhzCooperative ufsgveoeCompetitive wfCompetitive vfECompetitxenfxive yeyCompetitive gzCooperative eif{{fvfCooperative |fCooperative yew#Cooperative } euhs ~f shCompetitive y eCooperative vf|Competitepe~ive flCompetitive g{Competitive egg|ffCooperative fCooperative tg}Cooperative fh~eweCompetitive xfCompetitive he{  Competitfufive eCompetitive g}Cooperative exhfoeCooperative fCooperative rhz Cooperative Problem Set Week 3: Chapters 3 & 4 Chapter 3: Complete the EVEN numbers problems listed below; the problem set begins on page 100 in Gravetter and Wallnau (2013). The answers to the odd numbered problems are in the back of the book for additional practice. Provide the answer to each question number listed below using complete sentences in APA format. Steps completed to determine the answer may also be included. 2.) Why is it necessary to have more than one method for measuring central tendency? 4.) Find the mean, median, and mode for the following sample of scores: 8, 7, 8, 8, 4, 9, 10, 7, 8, 8, 9, 8, 6.) Find the mean, median, and mode for the scores in the following frequency distribution table: ____________ X f 10 1 9 2 8 3 7 3 6 4 5 2 ______________ 14.) A population of N = 20 scores has a mean of = 15. One score in the population is changed from X = 8 to X = 28. What is the value for the new population mean? 18.) One sample has a mean of M= 4 a second sample has a mean of M = 8. The two samples are combined into a single set of scores. a. What is the mean for the combined set if both the original sample have n = 7 scores? b. What is the mean for the combined set if the first sample has n = 3 and the second sample has n = 7? c. What is the mean for the combined set if the first sample has n = 7 and the second sample has n = 3? Additional Item: 1. Return to the four types of measurement scales (i.e., nominal, ordinal, interval and ratio) in Chapter 1 of Gravetter and Wallnau (2013). For each measurement scale select the most appropriated measures of central tendency. Also, for each measurement scale, identify any inappropriate measures of central tendency. Briefly explain your selections. Chapter 4: Complete the EVEN numbers problems listed below; the problem set begins on page 130 in Gravetter and Wallnau (2013). The answers to the odd numbered problems are in the back of the book for additional practice. Provide the answer to each question number listed below using complete sentences in APA format. Steps completed to determine the answer may also be included. 4.) What does it mean for a sample to have a standard deviation of zero? Describe the scores in such a sample. 6.) A population has a mean of = 80 and a standard deviation of = 20. a. Would a score of X = 70 be considered an extreme value (out in the tail) in this sample? b. If the standard deviation were =5, would a score of X = 70 be considered an extreme value? For Items 16 and 18, please show the steps taken (show your work): 16.) Calculate SS, variance, and standard deviation for the following sample of n = 4 scores: 7,4,2,1. (Note: The computational formula works well with these scores.) 18.) Calculate SS, variance, and standard deviation for the following population of N = 7 scores: 8, 1, 4, 3, 5, 3, 4. (Note: The definitional formula works well with these scores.) 20.) For the following population of N = 6 scores: 3, 1, 4, 3, 3, 4 a. Sketch a histogram showing the population distribution. b. Locate the value of the population mean in your sketch, and make an estimate of the standard deviation (as done in Example 4.2). c. Compute SS, variance, and standard deviation for the population. (How well does your estimate compare with the actual value of ?) 22.) In an extensive study involving thousands of British Children Arden and Plomin (2006) found significantly higher variance in the intelligence scores for males than for females. Following the hypothetical data, similar to the results obtained in the study. Note that the scores are not regular IQ scores but have been standardized so that the entire sample has a mean of M = 10 and a standard deviation of s = 12. a. Calculate the mean and the standard deviation for the sample of n = 8 females and for the sample of n = 8 males. b. Based on the means and the standard deviations, describe the differences in intelligence scores for male and females. _________________ Female Male_ 9 8 11 10 10 11 13 12 8 6 9 10 11 14 9 9 Additional Items: 1. Every population has a parametric mean () and parametric standard deviation (). Briefly discuss the impact of sample size on these parametric values. 2. Fact: by increasing sample size, the researcher does not reduce the size of the parametric standard deviation () but does decrease the uncertainty associated with the estimation of parametric values. Briefly explain the implications of this fact. 3. The concept of Degrees of Freedom re-appears throughout the study of statistics. Given a sample size of five (n=5), what are the degrees of freedom? Provide a detailed example using real numbers. Problem Set Week 4: Chapters 5 & 6 Chapter 5: Complete the EVEN numbers problems listed below; the problem set begins on page 161 in Gravetter and Wallnau (2013). The answers to the odd numbered problems are in the back of the book for additional practice. Provide the answer to each question number listed below using complete sentences in APA format. Steps completed to determine the answer may also be included. 4.) For a population with = 50 and = 8, a. Find the z - score for each of the following X values. (Note: You should be able to find these values using the definition of a z-score. You should not need to use a formula or do any serious calculations.) X = 54 X = 42 X= 62 X = 48 X = 52 X = 34 b. Find the score (X value) that corresponds to each of the following z-scores. (Again, you should be able to find these values without any formula or serious calculations.) z = 1.00 z = - 0.50 z = 0.75 z = - 0.25 z = 1.50 z = -1.50 8.) A sample has a mean of M = 40 and a standard deviation of s = 6. Find the z-score for each of the following X values from this sample. X = 44 X = 28 X = 42 X = 50 X = 46 X = 37 14.) For a population with a standard deviation of = 8, a score of X = 44 corresponds to z = - 0.50. What is the population mean? 18.) In a population of exam scores, a score of X = 48 corresponds to z = +1.00 and a score of X = 36 corresponds to z = -0.50. Find the mean and standard deviation for the population. (Hint: Sketch the distribution and locate the two scores on your sketch.) 22.) For each of the following, identify the exam score that should lead to the better grade. In each case, explain your answer.. a. A score of X = 56, on an exam with = 50 and = 4, or a score of X = 60 on an exam with = 50 and = 20. b. A score of X = 40, on an exam with = 45 and = 2; or a score of X = 60 on an exam with = 70 and = 20. c. A score of X = 62, on an exam with = 50 and = 8; or a score of X = 23 on an exam with =20 and = 2 Additional Item: 1. Review your response to item 22 above. Your principal is interested in seeing the relationship between performance on a summative (final) exam produced by the math teachers in your school and the state Common Core exam. How could z-scores be used to make this comparison for a selected group of 25 students in your school? (maximum 300 words) Chapter 6: Complete the EVEN numbers problems listed below; the problem set begins on page 196 in Gravetter and Wallnau (2013). The answers to the odd numbered problems are in the back of the book for additional practice. Provide the answer to each question number listed below using complete sentences in APA format. Steps completed to determine the answer may also be included. 2.) A psychology class consists of 14 males and 36 females. If the professor selects from the class list using random sampling, a. What is the probability that the first student selected will be a female? b. If a random sample of n = 3 students is selected and the first two are both females, what is the probability that the third student selected will be a male? 4.) What is sampling with replacement, and why is it used? 6.) Draw a vertical line through a normal distribution for each of the following z-score locations. Determine whether the body is on the right or left side of the line and find the proportion in the body.(Note: the word body in this item refers to the bulk of the observations.) a. b. c. d. z = 2.20 z= 1.60 z = -1.50 z = -0.70 8.) What proportion of a normal distribution is located between each of the following zscore boundaries? a. z = -0.50 and z = +0.50 b. z = -0.90 and z = + 0.90 c. z = -1.50 and z = + 1.50 d. 10.) Find the z -score location of a vertical line that separates a normal distribution as described in each of the following. a. 20% in the tail on the left b. 40% in the tail on the right c. 75% in the body on the left d. 99% in the body on the right 14.) IQ test scores are standardized to produce a normal distribution with a mean of = 100 and a standard deviation of =15. Find the proportion of the population ineach of the following IQ categories. a. Genius or near genius: IQ greater thank 140 b. Very superior intelligence: IQ between 120 and 140 c. Average or normal intelligence: IQ between 90 and 109 Additional Items: 1. For the following questions, a calculated probability of equal to or less than 0.05 is considered significant. a. Is it significant to get a 12 when a pair of dice is rolled? Show evidence and discuss. b. Assume a study of 500 randomly selected school bus routes revealed 480 arrived on time. Is it significant for a school bus to arrive late? Show evidence and discuss. 2. The following table is from the Social Security Actuarial Tables. For each age, it gives the probability of death within one year, the number of living out of an original 100,000 and the additional life expectancy for a person of this age. Determine the following using the table: a. To what age may a female of age 60 expected to live on the average? b. To what age is a male of age 70 expected to live on average? c. How many 60-year old females on average will be living at age 61? d. How many 70-year old males on average will be living at age 71? Age P(Death within one year) 10 20 30 40 50 0.000111 0.001287 0.001375 0.002542 0.005696 MALES Number of Living Life Expectancy P(Death within one year) 99,021 98,451 97,113 95,427 91,853 65.13 55.46 46.16 36.88 28.09 0.000105 0.000469 0.000627 0.001498 0.003240 FEMALES Number of Living Life Expectancy 99,217 98,950 98,431 97,513 95,378 70.22 60.40 50.69 41.11 31.91 60 70 80 90 0.012263 0.028904 0.071687 0.188644 84,692 70,214 44,272 12,862 20.00 12.98 7.43 3.68 0.007740 0.018938 0.049527 0.146696 90,847 80,583 594,31 24,331 23.21 15.45 9.00 4.45 SPSS Week 4 Imagine a researcher is interested in the relationships among teachers' self-esteem, perceptions of their principals' conflict management style, and productivity. A convenience sample of 40 teachers was used. These teachers completed a questionnaire including a number of demographic questions as well as measures to assess perceptions of principal conflict management style, self-esteem, and productivity. The researcher unfortunately experienced time management issues for this study; consequently, the literature to select measures was hurriedly reviewed. The following scores are from the self-esteem instrument (ScoreOne) using a 100point scale. Please use these data to complete the questions below (these data have already been entered in a SPSS file; see the note below the data table). . Self-esteem scores 1 64 68 74 75 76 79 80 82 68 70 74 76 78 79 82 85 71 73 75 77 78 80 83 86 73 74 77 77 78 81 84 87 77 71 75 76 79 83 89 91 After the researcher returned to the literature, a better measure of self-esteem was identified. The same sample of teachers completed the new self-esteem instrument (ScoreTwo) also using a 100-point scale. Here are their scores: Self-esteem scores 2 95 87 79 78 85 96 90 92 86 74 79 85 81 83 96 84 75 89 93 77 76 87 84 92 99 83 84 76 75 72 88 87 84 83 94 87 79 76 79 94 Download the SPSS data set: teachersurvey.sav. Not all of the variables in that SPSS file will be used for this assignment. Part of the goal of this activity is to explore the various tools under the ANALYZE tab in SPSS, the more exploring the more comfortable it will become. Please note in the data set the selfesteem scores are named simply ScoreOne and ScoreTwo. In this SPSS assignment, use the tools learned in this course thus far, with an emphasis on the tools acquired in Gravetter and Wallnau (2013) Chapters 5 and 6. 1.) For each set of self-esteem scores, create an SPSS output of the descriptive statistics with the mean and standard deviation of both self-esteem assessments. a.) What are the mean and standard deviation of self-esteem 1 and self-esteem 2 using APA style? b.) Participant 10's score on ScoreOne was 70. It was 74 on ScoreTwo. Using the mean and standard deviations from item 1.a, what steps (statistical tests) would be employed to compare these two scores? c.) Create frequency distribution histograms for both sets of data. Visually inspect the distributions and describe how they compare. How might the selected sample and the sample size influence the distributions? 2.) Transform the X values into z-scores and re-run the descriptive statistics for each set of self-esteem scores. a.) What are the mean and standard deviation for the standardized scores (zscores) for ScoreOne and ScoreTwo using APA style? Why were these values obtained? Provide a research example in your field where the use of standardized scores (z-scores) might be helpful. b.) Using standardized data (z-scores), can the individuals' scores on ScoreOne and ScoreTwo be compared? Why or why not? c.) Compare the histograms of the raw data to the standardized data. Provide SPSS output to support the answer. Problem Set Week 4: Chapters 5 & 6 Chapter 5: Complete the EVEN numbers problems listed below; the problem set begins on page 161 in Gravetter and Wallnau (2013). The answers to the odd numbered problems are in the back of the book for additional practice. Provide the answer to each question number listed below using complete sentences in APA format. Steps completed to determine the answer may also be included. 4.) For a population with = 50 and = 8, a. Find the z - score for each of the following X values. (Note: You should be able to find these values using the definition of a z-score. You should not need to use a formula or do any serious calculations.) X = 54 X = 42 X= 62 X = 48 X = 52 X = 34 b. Find the score (X value) that corresponds to each of the following z-scores. (Again, you should be able to find these values without any formula or serious calculations.) z = 1.00 z = - 0.50 z = 0.75 z = - 0.25 z = 1.50 z = -1.50 8.) A sample has a mean of M = 40 and a standard deviation of s = 6. Find the z-score for each of the following X values from this sample. X = 44 X = 28 X = 42 X = 50 X = 46 X = 37 14.) For a population with a standard deviation of = 8, a score of X = 44 corresponds to z = - 0.50. What is the population mean? 18.) In a population of exam scores, a score of X = 48 corresponds to z = +1.00 and a score of X = 36 corresponds to z = -0.50. Find the mean and standard deviation for the population. (Hint: Sketch the distribution and locate the two scores on your sketch.) 22.) For each of the following, identify the exam score that should lead to the better grade. In each case, explain your answer.. a. A score of X = 56, on an exam with = 50 and = 4, or a score of X = 60 on an exam with = 50 and = 20. b. A score of X = 40, on an exam with = 45 and = 2; or a score of X = 60 on an exam with = 70 and = 20. c. A score of X = 62, on an exam with = 50 and = 8; or a score of X = 23 on an exam with =20 and = 2 Additional Item: 1. Review your response to item 22 above. Your principal is interested in seeing the relationship between performance on a summative (final) exam produced by the math teachers in your school and the state Common Core exam. How could z-scores be used to make this comparison for a selected group of 25 students in your school? (maximum 300 words) Chapter 6: Complete the EVEN numbers problems listed below; the problem set begins on page 196 in Gravetter and Wallnau (2013). The answers to the odd numbered problems are in the back of the book for additional practice. Provide the answer to each question number listed below using complete sentences in APA format. Steps completed to determine the answer may also be included. 2.) A psychology class consists of 14 males and 36 females. If the professor selects from the class list using random sampling, a. What is the probability that the first student selected will be a female? b. If a random sample of n = 3 students is selected and the first two are both females, what is the probability that the third student selected will be a male? 4.) What is sampling with replacement, and why is it used? 6.) Draw a vertical line through a normal distribution for each of the following z-score locations. Determine whether the body is on the right or left side of the line and find the proportion in the body.(Note: the word body in this item refers to the bulk of the observations.) a. b. c. d. z = 2.20 z= 1.60 z = -1.50 z = -0.70 8.) What proportion of a normal distribution is located between each of the following zscore boundaries? a. z = -0.50 and z = +0.50 b. z = -0.90 and z = + 0.90 c. z = -1.50 and z = + 1.50 d. 10.) Find the z -score location of a vertical line that separates a normal distribution as described in each of the following. a. 20% in the tail on the left b. 40% in the tail on the right c. 75% in the body on the left d. 99% in the body on the right 14.) IQ test scores are standardized to produce a normal distribution with a mean of = 100 and a standard deviation of =15. Find the proportion of the population ineach of the following IQ categories. a. Genius or near genius: IQ greater thank 140 b. Very superior intelligence: IQ between 120 and 140 c. Average or normal intelligence: IQ between 90 and 109 Additional Items: 1. For the following questions, a calculated probability of equal to or less than 0.05 is considered significant. a. Is it significant to get a 12 when a pair of dice is rolled? Show evidence and discuss. b. Assume a study of 500 randomly selected school bus routes revealed 480 arrived on time. Is it significant for a school bus to arrive late? Show evidence and discuss. 2. The following table is from the Social Security Actuarial Tables. For each age, it gives the probability of death within one year, the number of living out of an original 100,000 and the additional life expectancy for a person of this age. Determine the following using the table: a. To what age may a female of age 60 expected to live on the average? b. To what age is a male of age 70 expected to live on average? c. How many 60-year old females on average will be living at age 61? d. How many 70-year old males on average will be living at age 71? Age P(Death within one year) 10 20 30 40 50 0.000111 0.001287 0.001375 0.002542 0.005696 MALES Number of Living Life Expectancy P(Death within one year) 99,021 98,451 97,113 95,427 91,853 65.13 55.46 46.16 36.88 28.09 0.000105 0.000469 0.000627 0.001498 0.003240 FEMALES Number of Living Life Expectancy 99,217 98,950 98,431 97,513 95,378 70.22 60.40 50.69 41.11 31.91 60 70 80 90 0.012263 0.028904 0.071687 0.188644 84,692 70,214 44,272 12,862 20.00 12.98 7.43 3.68 0.007740 0.018938 0.049527 0.146696 90,847 80,583 594,31 24,331 23.21 15.45 9.00 4.45 SPSS Week 4 Imagine a researcher is interested in the relationships among teachers' self-esteem, perceptions of their principals' conflict management style, and productivity. A convenience sample of 40 teachers was used. These teachers completed a questionnaire including a number of demographic questions as well as measures to assess perceptions of principal conflict management style, self-esteem, and productivity. The researcher unfortunately experienced time management issues for this study; consequently, the literature to select measures was hurriedly reviewed. The following scores are from the self-esteem instrument (ScoreOne) using a 100point scale. Please use these data to complete the questions below (these data have already been entered in a SPSS file; see the note below the data table). . Self-esteem scores 1 64 68 74 75 76 79 80 82 68 70 74 76 78 79 82 85 71 73 75 77 78 80 83 86 73 74 77 77 78 81 84 87 77 71 75 76 79 83 89 91 After the researcher returned to the literature, a better measure of self-esteem was identified. The same sample of teachers completed the new self-esteem instrument (ScoreTwo) also using a 100-point scale. Here are their scores: Self-esteem scores 2 95 87 79 78 85 96 90 92 86 74 79 85 81 83 96 84 75 89 93 77 76 87 84 92 99 83 84 76 75 72 88 87 84 83 94 87 79 76 79 94 Download the SPSS data set: teachersurvey.sav. Not all of the variables in that SPSS file will be used for this assignment. Part of the goal of this activity is to explore the various tools under the ANALYZE tab in SPSS, the more exploring the more comfortable it will become. Please note in the data set the selfesteem scores are named simply ScoreOne and ScoreTwo. In this SPSS assignment, use the tools learned in this course thus far, with an emphasis on the tools acquired in Gravetter and Wallnau (2013) Chapters 5 and 6. 1.) For each set of self-esteem scores, create an SPSS output of the descriptive statistics with the mean and standard deviation of both self-esteem assessments. a.) What are the mean and standard deviation of self-esteem 1 and self-esteem 2 using APA style? b.) Participant 10's score on ScoreOne was 70. It was 74 on ScoreTwo. Using the mean and standard deviations from item 1.a, what steps (statistical tests) would be employed to compare these two scores? c.) Create frequency distribution histograms for both sets of data. Visually inspect the distributions and describe how they compare. How might the selected sample and the sample size influence the distributions? 2.) Transform the X values into z-scores and re-run the descriptive statistics for each set of self-esteem scores. a.) What are the mean and standard deviation for the standardized scores (zscores) for ScoreOne and ScoreTwo using APA style? Why were these values obtained? Provide a research example in your field where the use of standardized scores (z-scores) might be helpful. b.) Using standardized data (z-scores), can the individuals' scores on ScoreOne and ScoreTwo be compared? Why or why not? c.) Compare the histograms of the raw data to the standardized data. Provide SPSS output to support the answer. Problem Set Week 3: Chapters 3 & 4 Chapter 3: Complete the EVEN numbers problems listed below; the problem set begins on page 100 in Gravetter and Wallnau (2013). The answers to the odd numbered problems are in the back of the book for additional practice. Provide the answer to each question number listed below using complete sentences in APA format. Steps completed to determine the answer may also be included. 2.) Why is it necessary to have more than one method for measuring central tendency? 4.) Find the mean, median, and mode for the following sample of scores: 8, 7, 8, 8, 4, 9, 10, 7, 8, 8, 9, 8, 6.) Find the mean, median, and mode for the scores in the following frequency distribution table: ____________ X f 10 1 9 2 8 3 7 3 6 4 5 2 ______________ 14.) A population of N = 20 scores has a mean of = 15. One score in the population is changed from X = 8 to X = 28. What is the value for the new population mean? 18.) One sample has a mean of M= 4 a second sample has a mean of M = 8. The two samples are combined into a single set of scores. a. What is the mean for the combined set if both the original sample have n = 7 scores? b. What is the mean for the combined set if the first sample has n = 3 and the second sample has n = 7? c. What is the mean for the combined set if the first sample has n = 7 and the second sample has n = 3? Additional Item: 1. Return to the four types of measurement scales (i.e., nominal, ordinal, interval and ratio) in Chapter 1 of Gravetter and Wallnau (2013). For each measurement scale select the most appropriated measures of central tendency. Also, for each measurement scale, identify any inappropriate measures of central tendency. Briefly explain your selections. Chapter 4: Complete the EVEN numbers problems listed below; the problem set begins on page 130 in Gravetter and Wallnau (2013). The answers to the odd numbered problems are in the back of the book for additional practice. Provide the answer to each question number listed below using complete sentences in APA format. Steps completed to determine the answer may also be included. 4.) What does it mean for a sample to have a standard deviation of zero? Describe the scores in such a sample. 6.) A population has a mean of = 80 and a standard deviation of = 20. a. Would a score of X = 70 be considered an extreme value (out in the tail) in this sample? b. If the standard deviation were =5, would a score of X = 70 be considered an extreme value? For Items 16 and 18, please show the steps taken (show your work): 16.) Calculate SS, variance, and standard deviation for the following sample of n = 4 scores: 7,4,2,1. (Note: The computational formula works well with these scores.) 18.) Calculate SS, variance, and standard deviation for the following population of N = 7 scores: 8, 1, 4, 3, 5, 3, 4. (Note: The definitional formula works well with these scores.) 20.) For the following population of N = 6 scores: 3, 1, 4, 3, 3, 4 a. Sketch a histogram showing the population distribution. b. Locate the value of the population mean in your sketch, and make an estimate of the standard deviation (as done in Example 4.2). c. Compute SS, variance, and standard deviation for the population. (How well does your estimate compare with the actual value of ?) 22.) In an extensive study involving thousands of British Children Arden and Plomin (2006) found significantly higher variance in the intelligence scores for males than for females. Following the hypothetical data, similar to the results obtained in the study. Note that the scores are not regular IQ scores but have been standardized so that the entire sample has a mean of M = 10 and a standard deviation of s = 12. a. Calculate the mean and the standard deviation for the sample of n = 8 females and for the sample of n = 8 males. b. Based on the means and the standard deviations, describe the differences in intelligence scores for male and females. _________________ Female Male_ 9 8 11 10 10 11 13 12 8 6 9 10 11 14 9 9 Additional Items: 1. Every population has a parametric mean () and parametric standard deviation (). Briefly discuss the impact of sample size on these parametric values. 2. Fact: by increasing sample size, the researcher does not reduce the size of the parametric standard deviation () but does decrease the uncertainty associated with the estimation of parametric values. Briefly explain the implications of this fact. 3. The concept of Degrees of Freedom re-appears throughout the study of statistics. Given a sample size of five (n=5), what are the degrees of freedom? Provide a detailed example using real numbers. Problem Set Week 4: Chapters 5 & 6 Chapter 5: Complete the EVEN numbers problems listed below; the problem set begins on page 161 in Gravetter and Wallnau (2013). The answers to the odd numbered problems are in the back of the book for additional practice. Provide the answer to each question number listed below using complete sentences in APA format. Steps completed to determine the answer may also be included. 4.) For a population with = 50 and = 8, a. Find the z - score for each of the following X values. (Note: You should be able to find these values using the definition of a z-score. You should not need to use a formula or do any serious calculations.) X = 54 X = 42 X= 62 X = 48 X = 52 X = 34 b. Find the score (X value) that corresponds to each of the following z-scores. (Again, you should be able to find these values without any formula or serious calculations.) z = 1.00 z = - 0.50 z = 0.75 z = - 0.25 z = 1.50 z = -1.50 8.) A sample has a mean of M = 40 and a standard deviation of s = 6. Find the z-score for each of the following X values from this sample. X = 44 X = 28 X = 42 X = 50 X = 46 X = 37 14.) For a population with a standard deviation of = 8, a score of X = 44 corresponds to z = - 0.50. What is the population mean? 18.) In a population of exam scores, a score of X = 48 corresponds to z = +1.00 and a score of X = 36 corresponds to z = -0.50. Find the mean and standard deviation for the population. (Hint: Sketch the distribution and locate the two scores on your sketch.) 22.) For each of the following, identify the exam score that should lead to the better grade. In each case, explain your answer.. a. A score of X = 56, on an exam with = 50 and = 4, or a score of X = 60 on an exam with = 50 and = 20. b. A score of X = 40, on an exam with = 45 and = 2; or a score of X = 60 on an exam with = 70 and = 20. c. A score of X = 62, on an exam with = 50 and = 8; or a score of X = 23 on an exam with =20 and = 2 Additional Item: 1. Review your response to item 22 above. Your principal is interested in seeing the relationship between performance on a summative (final) exam produced by the math teachers in your school and the state Common Core exam. How could z-scores be used to make this comparison for a selected group of 25 students in your school? (maximum 300 words) Chapter 6: Complete the EVEN numbers problems listed below; the problem set begins on page 196 in Gravetter and Wallnau (2013). The answers to the odd numbered problems are in the back of the book for additional practice. Provide the answer to each question number listed below using complete sentences in APA format. Steps completed to determine the answer may also be included. 2.) A psychology class consists of 14 males and 36 females. If the professor selects from the class list using random sampling, a. What is the probability that the first student selected will be a female? b. If a random sample of n = 3 students is selected and the first two are both females, what is the probability that the third student selected will be a male? 4.) What is sampling with replacement, and why is it used? 6.) Draw a vertical line through a normal distribution for each of the following z-score locations. Determine whether the body is on the right or left side of the line and find the proportion in the body.(Note: the word body in this item refers to the bulk of the observations.) a. b. c. d. z = 2.20 z= 1.60 z = -1.50 z = -0.70 8.) What proportion of a normal distribution is located between each of the following zscore boundaries? a. z = -0.50 and z = +0.50 b. z = -0.90 and z = + 0.90 c. z = -1.50 and z = + 1.50 d. 10.) Find the z -score location of a vertical line that separates a normal distribution as described in each of the following. a. 20% in the tail on the left b. 40% in the tail on the right c. 75% in the body on the left d. 99% in the body on the right 14.) IQ test scores are standardized to produce a normal distribution with a mean of = 100 and a standard deviation of =15. Find the proportion of the population ineach of the following IQ categories. a. Genius or near genius: IQ greater thank 140 b. Very superior intelligence: IQ between 120 and 140 c. Average or normal intelligence: IQ between 90 and 109 Additional Items: 1. For the following questions, a calculated probability of equal to or less than 0.05 is considered significant. a. Is it significant to get a 12 when a pair of dice is rolled? Show evidence and discuss. b. Assume a study of 500 randomly selected school bus routes revealed 480 arrived on time. Is it significant for a school bus to arrive late? Show evidence and discuss. 2. The following table is from the Social Security Actuarial Tables. For each age, it gives the probability of death within one year, the number of living out of an original 100,000 and the additional life expectancy for a person of this age. Determine the following using the table: a. To what age may a female of age 60 expected to live on the average? b. To what age is a male of age 70 expected to live on average? c. How many 60-year old females on average will be living at age 61? d. How many 70-year old males on average will be living at age 71? Age P(Death within one year) 10 20 30 40 50 0.000111 0.001287 0.001375 0.002542 0.005696 MALES Number of Living Life Expectancy P(Death within one year) 99,021 98,451 97,113 95,427 91,853 65.13 55.46 46.16 36.88 28.09 0.000105 0.000469 0.000627 0.001498 0.003240 FEMALES Number of Living Life Expectancy 99,217 98,950 98,431 97,513 95,378 70.22 60.40 50.69 41.11 31.91 60 70 80 90 0.012263 0.028904 0.071687 0.188644 84,692 70,214 44,272 12,862 20.00 12.98 7.43 3.68 0.007740 0.018938 0.049527 0.146696 90,847 80,583 594,31 24,331 23.21 15.45 9.00 4.45 SPSS Week 4 Imagine a researcher is interested in the relationships among teachers' self-esteem, perceptions of their principals' conflict management style, and productivity. A convenience sample of 40 teachers was used. These teachers completed a questionnaire including a number of demographic questions as well as measures to assess perceptions of principal conflict management style, self-esteem, and productivity. The researcher unfortunately experienced time management issues for this study; consequently, the literature to select measures was hurriedly reviewed. The following scores are from the self-esteem instrument (ScoreOne) using a 100point scale. Please use these data to complete the questions below (these data have already been entered in a SPSS file; see the note below the data table). . Self-esteem scores 1 64 68 74 75 76 79 80 82 68 70 74 76 78 79 82 85 71 73 75 77 78 80 83 86 73 74 77 77 78 81 84 87 77 71 75 76 79 83 89 91 After the researcher returned to the literature, a better measure of self-esteem was identified. The same sample of teachers completed the new self-esteem instrument (ScoreTwo) also using a 100-point scale. Here are their scores: Self-esteem scores 2 95 87 79 78 85 96 90 92 86 74 79 85 81 83 96 84 75 89 93 77 76 87 84 92 99 83 84 76 75 72 88 87 84 83 94 87 79 76 79 94 Download the SPSS data set: teachersurvey.sav. Not all of the variables in that SPSS file will be used for this assignment. Part of the goal of this activity is to explore the various tools under the ANALYZE tab in SPSS, the more exploring the more comfortable it will become. Please note in the data set the selfesteem scores are named simply ScoreOne and ScoreTwo. In this SPSS assignment, use the tools learned in this course thus far, with an emphasis on the tools acquired in Gravetter and Wallnau (2013) Chapters 5 and 6. 1.) For each set of self-esteem scores, create an SPSS output of the descriptive statistics with the mean and standard deviation of both self-esteem assessments. a.) What are the mean and standard deviation of self-esteem 1 and self-esteem 2 using APA style? b.) Participant 10's score on ScoreOne was 70. It was 74 on ScoreTwo. Using the mean and standard deviations from item 1.a, what steps (statistical tests) would be employed to compare these two scores? c.) Create frequency distribution histograms for both sets of data. Visually inspect the distributions and describe how they compare. How might the selected sample and the sample size influence the distributions? 2.) Transform the X values into z-scores and re-run the descriptive statistics for each set of self-esteem scores. a.) What are the mean and standard deviation for the standardized scores (zscores) for ScoreOne and ScoreTwo using APA style? Why were these values obtained? Provide a research example in your field where the use of standardized scores (z-scores) might be helpful. b.) Using standardized data (z-scores), can the individuals' scores on ScoreOne and ScoreTwo be compared? Why or why not? c.) Compare the histograms of the raw data to the standardized data. Provide SPSS output to support the answer. Problem Set Week 4: Chapters 5 & 6 Chapter 5: Complete the EVEN numbers problems listed below; the problem set begins on page 161 in Gravetter and Wallnau (2013). The answers to the odd numbered problems are in the back of the book for additional practice. Provide the answer to each question number listed below using complete sentences in APA format. Steps completed to determine the answer may also be included. 4.) For a population with = 50 and = 8, a. Find the z - score for each of the following X values. (Note: You should be able to find these values using the definition of a z-score. You should not need to use a formula or do any serious calculations.) X = 54 X = 42 X= 62 X = 48 X = 52 X = 34 b. Find the score (X value) that corresponds to each of the following z-scores. (Again, you should be able to find these values without any formula or serious calculations.) z = 1.00 z = - 0.50 z = 0.75 z = - 0.25 z = 1.50 z = -1.50 8.) A sample has a mean of M = 40 and a standard deviation of s = 6. Find the z-score for each of the following X values from this sample. X = 44 X = 28 X = 42 X = 50 X = 46 X = 37 14.) For a population with a standard deviation of = 8, a score of X = 44 corresponds to z = - 0.50. What is the population mean? 18.) In a population of exam scores, a score of X = 48 corresponds to z = +1.00 and a score of X = 36 corresponds to z = -0.50. Find the mean and standard deviation for the population. (Hint: Sketch the distribution and locate the two scores on your sketch.) 22.) For each of the following, identify the exam score that should lead to the better grade. In each case, explain your answer.. a. A score of X = 56, on an exam with = 50 and = 4, or a score of X = 60 on an exam with = 50 and = 20. b. A score of X = 40, on an exam with = 45 and = 2; or a score of X = 60 on an exam with = 70 and = 20. c. A score of X = 62, on an exam with = 50 and = 8; or a score of X = 23 on an exam with =20 and = 2 Additional Item: 1. Review your response to item 22 above. Your principal is interested in seeing the relationship between performance on a summative (final) exam produced by the math teachers in your school and the state Common Core exam. How could z-scores be used to make this comparison for a selected group of 25 students in your school? (maximum 300 words) Chapter 6: Complete the EVEN numbers problems listed below; the problem set begins on page 196 in Gravetter and Wallnau (2013). The answers to the odd numbered problems are in the back of the book for additional practice. Provide the answer to each question number listed below using complete sentences in APA format. Steps completed to determine the answer may also be included. 2.) A psychology class consists of 14 males and 36 females. If the professor selects from the class list using random sampling, a. What is the probability that the first student selected will be a female? b. If a random sample of n = 3 students is selected and the first two are both females, what is the probability that the third student selected will be a male? 4.) What is sampling with replacement, and why is it used? 6.) Draw a vertical line through a normal distribution for each of the following z-score locations. Determine whether the body is on the right or left side of the line and find the proportion in the body.(Note: the word body in this item refers to the bulk of the observations.) a. b. c. d. z = 2.20 z= 1.60 z = -1.50 z = -0.70 8.) What proportion of a normal distribution is located between each of the following zscore boundaries? a. z = -0.50 and z = +0.50 b. z = -0.90 and z = + 0.90 c. z = -1.50 and z = + 1.50 d. 10.) Find the z -score location of a vertical line that separates a normal distribution as described in each of the following. a. 20% in the tail on the left b. 40% in the tail on the right c. 75% in the body on the left d. 99% in the body on the right 14.) IQ test scores are standardized to produce a normal distribution with a mean of = 100 and a standard deviation of =15. Find the proportion of the population ineach of the following IQ categories. a. Genius or near genius: IQ greater thank 140 b. Very superior intelligence: IQ between 120 and 140 c. Average or normal intelligence: IQ between 90 and 109 Additional Items: 1. For the following questions, a calculated probability of equal to or less than 0.05 is considered significant. a. Is it significant to get a 12 when a pair of dice is rolled? Show evidence and discuss. b. Assume a study of 500 randomly selected school bus routes revealed 480 arrived on time. Is it significant for a school bus to arrive late? Show evidence and discuss. 2. The following table is from the Social Security Actuarial Tables. For each age, it gives the probability of death within one year, the number of living out of an original 100,000 and the additional life expectancy for a person of this age. Determine the following using the table: a. To what age may a female of age 60 expected to live on the average? b. To what age is a male of age 70 expected to live on average? c. How many 60-year old females on average will be living at age 61? d. How many 70-year old males on average will be living at age 71? Age P(Death within one year) 10 20 30 40 50 0.000111 0.001287 0.001375 0.002542 0.005696 MALES Number of Living Life Expectancy P(Death within one year) 99,021 98,451 97,113 95,427 91,853 65.13 55.46 46.16 36.88 28.09 0.000105 0.000469 0.000627 0.001498 0.003240 FEMALES Number of Living Life Expectancy 99,217 98,950 98,431 97,513 95,378 70.22 60.40 50.69 41.11 31.91 60 70 80 90 0.012263 0.028904 0.071687 0.188644 84,692 70,214 44,272 12,862 20.00 12.98 7.43 3.68 0.007740 0.018938 0.049527 0.146696 90,847 80,583 594,31 24,331 23.21 15.45 9.00 4.45 SPSS Week 4 Imagine a researcher is interested in the relationships among teachers' self-esteem, perceptions of their principals' conflict management style, and productivity. A convenience sample of 40 teachers was used. These teachers completed a questionnaire including a number of demographic questions as well as measures to assess perceptions of principal conflict management style, self-esteem, and productivity. The researcher unfortunately experienced time management issues for this study; consequently, the literature to select measures was hurriedly reviewed. The following scores are from the self-esteem instrument (ScoreOne) using a 100point scale. Please use these data to complete the questions below (these data have already been entered in a SPSS file; see the note below the data table). . Self-esteem scores 1 64 68 74 75 76 79 80 82 68 70 74 76 78 79 82 85 71 73 75 77 78 80 83 86 73 74 77 77 78 81 84 87 77 71 75 76 79 83 89 91 After the researcher returned to the literature, a better measure of self-esteem was identified. The same sample of teachers completed the new self-esteem instrument (ScoreTwo) also using a 100-point scale. Here are their scores: Self-esteem scores 2 95 87 79 78 85 96 90 92 86 74 79 85 81 83 96 84 75 89 93 77 76 87 84 92 99 83 84 76 75 72 88 87 84 83 94 87 79 76 79 94 Download the SPSS data set: teachersurvey.sav. Not all of the variables in that SPSS file will be used for this assignment. Part of the goal of this activity is to explore the various tools under the ANALYZE tab in SPSS, the more exploring the more comfortable it will become. Please note in the data set the selfesteem scores are named simply ScoreOne and ScoreTwo. In this SPSS assignment, use the tools learned in this course thus far, with an emphasis on the tools acquired in Gravetter and Wallnau (2013) Chapters 5 and 6. 1.) For each set of self-esteem scores, create an SPSS output of the descriptive statistics with the mean and standard deviation of both self-esteem assessments. a.) What are the mean and standard deviation of self-esteem 1 and self-esteem 2 using APA style? b.) Participant 10's score on ScoreOne was 70. It was 74 on ScoreTwo. Using the mean and standard deviations from item 1.a, what steps (statistical tests) would be employed to compare these two scores? c.) Create frequency distribution histograms for both sets of data. Visually inspect the distributions and describe how they compare. How might the selected sample and the sample size influence the distributions? 2.) Transform the X values into z-scores and re-run the descriptive statistics for each set of self-esteem scores. a.) What are the mean and standard deviation for the standardized scores (zscores) for ScoreOne and ScoreTwo using APA style? Why were these values obtained? Provide a research example in your field where the use of standardized scores (z-scores) might be helpful. b.) Using standardized data (z-scores), can the individuals' scores on ScoreOne and ScoreTwo be compared? Why or why not? c.) Compare the histograms of the raw data to the standardized data. Provide SPSS output to support the