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Statistics For The Behavioral Sciences 9th Edition Frederick J Gravetter, Larry B. Wallnau - Solutions

A researcher plans to compare two treatment conditions by measuring one sample in treatment 1 and a second sample in treatment 2. The researcher then compares the scores for the two treatments and finds a difference between the two groups. a. Briefly explain how the difference may have been caused
Describe the data for a correlational research study. Explain how these data are different from the data obtained in experimental and non-experimental studies, which also evaluate relationships between two variables?
Describe how the goal of an experimental research study is different from the goal for non-experimental or correlational research. Identify the two elements that are necessary for an experiment to achieve its goal?
Strack, Martin, and Stepper (1988) found that people rated cartoons as funnier when holding a pen in their teeth (which forced them to smile) than when holding a pen in their lips (which forced them to frown). For this study, identify the independent variable and the dependent variable?
Judge and Cable (2010) found that thin women had higher incomes than heavier women. Is this an example of an experimental or a non-experimental study?
Two researchers are both interested in the relationship between caffeine consumption and activity level for elementary school children. Each obtains a sample of n = 20 children. a. The first researcher interviews each child to determine the level of caffeine consumption. The researcher then records
Place the following sample of n = 20 scores in a frequency distribution table.
For the following set of quiz scores:a. Construct a frequency distribution table to organize the scores. b. Draw a frequency distribution histogram for these data?
Sketch a histogram and a polygon showing the distribution of scores presented in the following table: X _____________ f 7 .................... 1 6 .................... 1 5 .................... 3 4 .................... 6 3 .................... 4 2 .................... 1
A survey given to a sample of 200 college students contained questions about the following variables. For each variable, identify the kind of graph that should be used to display the distribution of scores (histogram, polygon, or bar graph). a. Number of pizzas consumed during the previous week b.
Each year the college gives away T-shirts to new students during freshman orientation. The students are allowed to pick the shirt sizes that they want. To determine how many of each size shirt they should order, college officials look at the distribution from last year. The following table shows
A report from the college dean indicates that for the previous semester, the grade distribution for the Department of Psychology included 135 As, 158 Bs, 140 Cs, 94 Ds, and 53 Fs. Determine what kind of graph would be appropriate for showing this distribution and sketch the frequency distribution
For the following set of scoresa. Place the scores in a frequency distribution table. b. Identify the shape of the distribution?
Place the following scores in a frequency distribution table. Based on the frequencies, what is the shape of the distribution?
For the following set of scores:a. Construct a frequency distribution table. b. Sketch a polygon showing the distribution. c. Describe the distribution using the following characteristics: (1) What is the shape of the distribution? (2) What score best identifies the center (average) for the
Fowler and Christakis (2008) report that personal happiness tends to be associated with having a social network including many other happy friends. To test this claim, a researcher obtains a sample of n = 16 adults who claim to be happy people and a similar sample of n = 16 adults who describe
Complete the final two columns in the following frequency distribution table and then find the percentiles and percentile ranks requested.a. What is the percentile rank for X = 2.5? b. What is the percentile rank for X = 6.5? c. What is the 20th percentile? d. What is the 80th percentile?
Construct a frequency distribution table for the following set of scores. Include columns for proportion and percentage in your table.
Complete the final two columns in the following frequency distribution table and then find the percentiles and percentile ranks requested.a. What is the percentile rank for X = 9.5? b. What is the percentile rank for X = 39.5? c. What is the 25th percentile? d. What is the 50th percentile?
Complete the final two columns in the following frequency distribution table and then use interpolation to find the percentiles and percentile ranks requested.a. What is the percentile rank for X = 6? b. What is the percentile rank for X = 9? c. What is the 25th percentile? d. What is the 90th
Find the requested percentiles and percentile ranks for the following distribution of quiz scores for a class of N = 40 students.a. What is the percentile rank for X = 15? b. What is the percentile rank for X = 18? c. What is the 15th percentile? d. What is the 90th percentile?
Use interpolation to find the requested percentiles and percentile ranks requested for the following distribution of scores.a. What is the percentile rank for X = 5? b. What is the percentile rank for X = 12? c. What is the 25th percentile? d. What is the 70th percentile?
The following frequency distribution presents a set of exam scores for a class of N = 20 students.a. Find the 30th percentile. b. Find the 88th percentile. c. What is the percentile rank for X = 77? d. What is the percentile rank for X = 90?
Construct a stem and leaf display for the data in problem 6 using one stem for the scores in the 60s, one for scores in the 50s, and so on?
A set of scores has been organized into the following stem and leaf display. For this set of scores: a. How many scores are in the 70s? b. Identify the individual scores in the 70s. c. How many scores are in the 40s? d. Identify the individual scores in the 40s. 3 ........... 8 4 ......... 60 5
Use a stem and leaf display to organize the following distribution of scores. Use seven stems with each stem corresponding to a 10-point interval.
Find each value requested for the distribution of scores in the following table.a. nb. ΣXc. ΣX2X ______________ f5 ..................... 24 ..................... 33 ..................... 52 ..................... 11 ..................... 1
Find each value requested for the distribution of scores in the following table.a. nb. ΣXc. ΣX2X _______________ f5 ........................ 14 ....................... 23 ....................... 32 ....................... 51 ....................... 3
For the following scores, the smallest value is X = 8 and the largest value is X = 29. Place the scores in a grouped frequency distribution tablea. Using an interval width of 2 points.b. Using an interval width of 5 points.
The following scores are the ages for a random sample of n = 30 drivers who were issued speeding tickets in New York during 2008. Determine the best interval width and place the scores in a grouped frequency distribution table. From looking at your table, does it appear that tickets are issued
For each of the following samples, determine the interval width that is most appropriate for a grouped frequency distribution and identify the approximate number of intervals needed to cover the range of scores. a. Sample scores range from X = 24 to X = 41 b. Sample scores range from X = 46 to X =
What information can you obtain about the scores in a regular frequency distribution table that is not available from a grouped table? Discuss.
Describe the difference in appearance between a bar graph and a histogram and describe the circumstances in which each type of graph is used?
What general purpose is served by a good measure of central tendency?
A sample of n = 8 scores has a mean of M = 10. If one new person with a score of X = 1 is added to the sample, what is the value for the new mean?
A sample of n = 5 scores has mean of M = 12. If one person with score of X = 8 is removed from the sample, what is the value for the new mean?
A sample of n = 11 scores has a mean of M = 4. One person with a score of X = 16 is added to the sample. What is the value for the new sample mean?
A sample of n = 9 scores has a mean of M = 10. One person with a score of X = 2 is removed from the sample. What is the value for the new sample mean?
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?
A sample of n = 7 scores has a mean of M = 9. One score in the sample is changed from X = 19 to X = 5. What is the value for the new sample mean?
A sample of n = 7 scores has a mean of M = 5. After one new score is added to the sample, the new mean is found to be M = 6. What is the value of the new score?
A population of N = 16 scores has a mean of µ = 20. After one score is removed from the population, the new mean is found to be µ = 19. What is the value of the score that was removed?
One sample has a mean of M = 4 and 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 of the original samples have n = 7 scores? b. What is the mean for the combined set if the first sample has n = 3 and
One sample has a mean of M = 5 and a second sample has a mean of M = 10. The two samples are combined into a single set of scores. a. What is the mean for the combined set if both of the original samples have n = 5 scores? b. What is the mean for the combined set if the first sample has n = 4
Why is it necessary to have more than one method for measuring central tendency? Discuss.
Explain why the mean is often not a good measure of central tendency for a skewed distribution?
Identify the circumstances in which the median rather than the mean is the preferred measure of central tendency?
For each of the following situations, identify the measure of central tendency (mean, median, or mode) that would provide the best description of the average score: a. A news reporter interviewed people shopping in a local mall and asked how much they spent on summer vacations. Most people traveled
One question on a student survey asks: In a typical week, how many times do you eat at a fast-food restaurant? The following frequency distribution table summarizes the results for a sample of n = 20 students. Number of times per week _____________ f 5 or more
A nutritionist studying weight gain for college freshmen obtains a sample of n = 20 first-year students at the state college. Each student is weighed on the first day of school and again on the last day of the semester. The following scores measure the change in weight, in pounds, for each student.
Does it ever seem to you that the weather is nice during the work week, but lousy on the weekend? Cerveny and Balling (1998) have confirmed that this is not your imagination-pollution accumulating during the work week most likely spoils the weekend weather for people on the Atlantic coast. Consider
Find the mean, median, and mode for the following sample of scores:
Find the mean, median, and mode for the following sample of scores:
Find the mean, median, and mode for the scores in the following frequency distribution table: X ___________ f 8 .................. 1 7 .................. 4 6 .................. 2 5 .................. 2 4 .................. 2 3 .................. 1
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
For the following samplea. Assume that the scores are measurements of a continuous variable and find the median by locating the precise midpoint of the distribution.b. Assume that the scores are measurements of a discrete variable and find the median.
A sample of n = 7 scores has a mean of M = 9. What is the value of ΣX for this sample?
A population with a mean of µ = 10 has ΣX = 250. How many scores are in the population?
a. What is the general goal for descriptive statistics?b. How is the goal served by putting scores in a frequency distribution?c. How is the goal served by computing a measure of central tendency?d. How is the goal served by computing a measure of variability?
In a classic study examining the relationship between heredity and intelligence, Robert Tryon (1940) used a selective breeding program to develop separate strains of "smart rats" and "dumb rats." Tryon started with a large sample of laboratory rats and tested each animal on a maze-learning problem.
In words, explain what is measured by each of the following: a. SS b. Variance c. Standard deviation?
A student was asked to compute the mean and standard deviation for the following sample of n = 5 scores: 81, 87, 89, 86, and 87. To simplify the arithmetic, the student first subtracted 80 points from each score to obtain a new sample consisting of 1, 7, 9, 6, and 7. The mean and standard deviation
For the following population of N = 6 scores:a. Calculate the range and the standard deviation. (Use either definition for the range.) b. Add 2 points to each score and compute the range and standard deviation again. Describe how adding a constant to each score influences measures of variability?
There are two different formulas or methods that can be used to calculate SS. a. Under what circumstances is the definitional formula easy to use? b. Under what circumstances is the computational formula preferred?
Calculate the mean and SS (sum of squared deviations) for each of the following samples. Based on the value for the mean, you should be able to decide which SS formula is better to use.
The range is completely determined by the two extreme scores in a distribution. The standard deviation, on the other hand, uses every score.a. Compute the range (choose either definition) and the standard deviation for the following sample of n = 5 scores. Note that there are three scores clustered
For the data in the following sample:a. Find the mean and the standard deviation. b. Now change the score of X = 8 to X = 18, and find the new mean and standard deviation. c. Describe how one extreme score influences the mean and standard deviation?
Calculate SS, variance, and standard deviation for the following sample of n = 4 scores: 7, 4, 2, 1. (The computational formula works well with these scores.)
Calculate SS, variance, and standard deviation for the following population of N = 8 scores: 0, 0, 5, 0, 3, 0, 0, 4. (The computational formula works well with these scores.)
Calculate SS, variance, and standard deviation for the following population of N = 7 scores: 8, 1, 4, 3, 5, 3, 4. (The definitional formula works well with these scores.)
Calculate SS, variance, and standard deviation for the following sample of n = 5 scores: 9, 6, 2, 2, 6. (The definitional formula works well with these scores.)
Can SS ever have a value less than zero? Explain your answer.
For the following population of N = 6 scores: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
For the following sample of n = 7 scores:a. Sketch a histogram showing the sample distribution.b. Locate the value of the sample mean in your sketch, and make an estimate of the standard deviation (as done in Example 4.5).c. Compute SS, variance, and standard deviation for the sample. (How well
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 are hypothetical data, similar to the results obtained in the study. Note that the scores are not regular IQ
In the Preview section at the beginning of this chapter we reported a study by Wegesin and Stern (2004) that found greater consistency (less variability) in the memory performance scores for younger women than for older women. The following data represent memory scores obtained for two women, one
Is it possible to obtain a negative value for the variance or the standard deviation?
What does it mean for a sample to have a standard deviation of zero? Describe the scores in such a sample.
Explain why the formulas for sample variance and population variance are different?
A population has a mean of µ = 80 and a standard deviation of µ = 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 µ = 5, would a score of X = 70 be considered an extreme value?
On an exam with a mean of M = 78, you obtain a score of X = 84. a. Would you prefer a standard deviation of s = 2 or s = 10? b. If your score were X = 72, would you prefer s = 2 or s = 10? Explain your answer.
A population has a mean of μ = 30 and a standard deviation of μ = 5.a. If 5 points were added to every score in the population, what would be the new values for the mean and standard deviation?b. If every score in the population were multiplied by 3 what would be the new values for the mean and
a. After 3 points have been added to every score in a sample, the mean is found to be M = 83 and the standard deviation is s = 8. What were the values for the mean and standard deviation for the original sample? b. After every score in a sample has been multiplied by 4, the mean is found to be M =
What information is provided by the sign (+/-) of a z-score? What information is provided by the numerical value of the z-score?
Find the z-score corresponding to a score of X = 60 for each of the following distributions.a. µ = 50 and σ = 20b. µ = 50 and σ = 10c. µ = 50 and σ = 5d. µ = 50 and σ = 2
Find the X value corresponding to z = 0.25 for each of the following distributions.a. µ = 40 and σ = 4b. µ = 40 and σ = 8c. µ = 40 and σ = 12d. µ = 40 and σ = 20
A score that is 6 points below the mean corresponds to a z-score of z = -0.50. What is the population standard deviation?
A score that is 12 points above the mean corresponds to a z-score of z = 3.00. What is the population standard deviation?
For a population with a standard deviation of σ = 8, a score of X = 44 corresponds to z = - 0.50. What is the population mean?
For a sample with a standard deviation of s = 10, a score of X = 65 corresponds to z = 1.50. What is the sample mean?
For a sample with a mean of µ = 45, a score of X = 59 corresponds to z = 2.00. What is the sample standard deviation?
For a population with a mean of µ = 70, a score of X = 62 corresponds to z = -2.00. What is the population standard deviation?
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?
In a distribution of scores, X = 64 corresponds to z = 1.00, and X = 67 corresponds to z = 2.00. Find the mean and standard deviation for the distribution?
A distribution has a standard deviation of σ = 12. Find the z-score for each of the following locations in the distribution.a. Above the mean by 3 points.b. Above the mean by 12 points.c. Below the mean by 24 points.d. Below the mean by 18 points.
For each of the following populations, would a score of X = 50 be considered a central score (near the middle of the distribution) or an extreme score (far out in the tail of the distribution)?a. µ = 45 and σ = 10b. µ and σ = 2c. µ = 90 and σ = 20d. µ = 60 and σ = 20
A distribution of exam scores has a mean of µ = 80.a. If your score is X = 86, which standard deviation would give you a better grade: σ = 4 σ = 8?b. If your score is X = 74, which standard deviation would give you a better grade: σ = 4 or σ = 8?
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 µ = 50 and σ = 4; or a score of X = 60 on an exam with µ = 50 and σ = 20.b. A score of X = 40, on an exam with µ = 45 and σ = 2; or
A distribution with a mean of µ = 62 and a standard deviation of σ = 8 is transformed into a standardized distribution with µ = 100 and σ = 20. Find the new, standardized score for each of the following values from the original population.a. X = 60b. X = 54c. X = 72d. X = 66
A distribution with a mean of µ = 56 and a standard deviation of σ = 20 is transformed into a standardized distribution with µ = 50 and σ = 10. Find the new, standardized score for each of the following values from the original population.a. X = 46b. X = 76c. X = 40d. X = 80

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