Questions and Answers of Statistics Behavioral Sciences

(a) Why does the size of the CI become larger when we change from a 95% CI to a 99% CI?(b) We can be more certain that the unknown population mean falls within the 99% CI than within the 95% CI. Why,
Use your statistical package to perform a one-sample t test to determine whether the average postquiz heart rate of Ihno's female students differs significantly (α = .05) from the mean resting HR
(a) What happens to the size of a CI as the standard error of the mean becomes larger? Why?(b) What happens to the size of a CI as the sample size becomes larger? Why?(c) What are the advantages of
Use your statistical package to perform a one-sample t test to determine whether the average baseline heart rate of Ihno's male students differs significantly from the mean HR (μ = 70) for
What advantages do confidence intervals have over testing a specific null hypothesis?
Use your statistical package to perform a one-sample t test to determine whether the baseline anxiety of Ihno's students differs significantly (α = .05) from the mean (μ = 18) found by a very large
You are drawing inferences about the mean of one population.(a) When should you use the t distributions as the theoretical model rather than the normal curve model?(b) Why is there a different
(a) What is the difference between a one-tailed test of significance and a two-tailed test of significance?(b) What are the disadvantages of using one-tailed tests of significance? Of using
The probability of making a Type I error when using the .01 criterion of significance is lower than when using the .05 criterion of significance. Why, then, don't researchers always use the .01
You are using the .05 criterion of significance.(a) If the two-tailed p value (i.e., the probability of obtaining the results you got if H0 is true and the hypothesized value of the population mean
(a) What is the difference between the standard deviation of a set of scores and the standard error of the mean?(b) Do behavioral science researchers want the standard error of the mean to be small
Which of the following are random samples from the specified populations and which are not? Why?(a) An experimenter selects every 10th name in the telephone book for her city, starting with one name
Repeat Exercise 3 for the women in Ihno's statistics class.Data from exercise 3Given that for SAT scores, μ = 500 and σ = 100:
(a) What is a random sample?(b) Why are random samples desirable in behavioral science research?(c) Why is it often difficult or impossible to obtain a sample that is truly random?
Assuming that the mean resting heart rate for all college-aged men (μ) is 70 bpm, with σ = 6, what is the z score for the baseline HR of the men in Ihno's data set? What are the one- and two-tailed
(a) Do researchers in the behavioral sciences want to draw conclusions about populations or about samples? Why?(b) Why, then, must researchers use samples?(c) What problems are caused by having to
Assuming that a normative study has shown that the mean anxiety level for college students (μ) is 18 (σ = 11) on the scale that Ihno used, what is the z score for the baseline anxiety scores in
If you know that a distribution of scores is bimodal, or asymmetric, or a J-curve, or any other shape that departs significantly from the normal distribution, would it be correct to use Table A to
Suppose that in the previous question, the SD of each exam is changed to 3. How would this affect the likelihood that there are scores on the first exam that are greater than the mean of the second
The distributions of scores on two exams are approximately normal. The mean of the first exam is 80, and the mean of the second exam is 95. The SD of each exam is 15. Draw a figure to show that there
Why is Table A given in terms of z scores rather than raw scores? Table A .00 .01 .02 .03 .04 .05 .06 .07 .08 .09 0.0 00.00 00.40 00.80 01.20 01.60 01.99 02.39 02.79 03.19 03.59 0.1 03.98 04.38
Repeat Exercise 2 for the statistics quiz score that was part of Ihno's experiment.Data from exercise 2Use your statistical package to create a z-score variable corresponding to the math background
For the same exams as in the previous question, another student scores 91 on the psychology exam and 93 on the English exam. He concludes that he did better on the English exam because his English
Use your statistical package to create a z-score variable corresponding to the math background quiz score, and then transform the z-score variable to a T score, an SAT score, and an IQ score.
A college student takes two introductory courses for first-year students. On her psychology exam, she scores 73; the mean is 81.0, and the SD is 5.0. On her English exam, she scores 67; the mean is
Use your statistical package to create new variables consisting of the z scores for the anxiety and heart rate measures both at baseline and prequiz in Ihno's data set. Request means and standard
What are the advantages of having a set of scores that has a mean of zero and a standard deviation of 1 (z scores)?
(a) When is it desirable to use the SIQR as the measure of variability?(b) When is it desirable to use the mean deviation (MD) as the measure of variability?
If the standard deviation of a set of scores is zero, what does this imply about the scores? Can a standard deviation be negative? Why or why not?
(a) When computing the standard deviation of a set of scores, when do we divide by N, and when do we divide by N − 1?(b) What is the difference between σ and s?
Use your statistical package to create a new variable that adds 50 points to the math quiz score. How have the measures of variability changed for this new variable as compared to the same measures
The mean of a statistics examination is 77.0.(a) If your score is 85, would you prefer the standard deviation to be large or small for purposes of getting a better grade? Why?(b) If your score is 69,
Use your statistical package to create a new variable that is equal to 2 times the diagnostic quiz score, so that the new variable is measured on a 0 to 100 scale. How do the measures of variability
Why is the range much less informative (and much less useful) as a measure of variability than the standard deviation? Give an example of when the range could really be useful.
Use your statistical package to find the range, semi-interquartile range, unbiased variance, and unbiased standard deviation for each of the quantitative variables in Ihno's data set. (Does your
Consider the following set of data, which represents 15 scores on a 10-point quiz: 0, 1, 3, 3, 4, 4, 4, 5, 5, 5, 7, 8, 9, 9, 10.(a) If the score of 10 is changed to 225,000,000, but the other numbers
(a) In a positively skewed distribution, which is larger, the mean or the median?(b) In a negatively skewed distribution, which is larger, the mean or the median?(c) In a symmetric distribution (such
Use your statistical package to find the mode, median, and mean for each of the quantitative variables in Ihno's data set.
For each of the following problems, which measure of central tendency should be computed?(a) An experimental psychologist wants a measure of central tendency for the number of trials taken to learn a
Rachel's percentile rank on a psychology test is 93. Darcy's percentile rank on a physics test is 80. Why is it potentially incorrect to conclude that Rachel did better than Darcy?
Repeat Exercise 8 separately for male and female students.Data from exercise 8Request the quartiles for the variables Baseline Anxiety and Prequiz Anxiety for all students. Describe the shift in
For each of the following, state which one represents better performance or if they are the same:(a) The 3rd quartile and the 70th percentile.(b) The 1st quartile and the 3rd decile.(c) The median
Request the quartiles for the variables Baseline Anxiety and Prequiz Anxiety for all students. Describe the shift in anxiety scores between these two measurement points.
What is the difference between a percentile rank and a percentile?
Request the deciles for the variable Quiz Score across all students.
Why might you want to convert a raw score into a percentile rank?
Request a stem-and-leaf plot for the variables Baseline Anxiety and Baseline Heart Rate for all students. Did your statistical package use the stem-and-leaf arrangement that you would have used for
What is a bimodal distribution? If a distribution of grades in a college course is bimodal, what does this imply about the students who took the course?
Repeat Exercise 4 separately for male and female students. Describe the shapes of all four of the resulting distributions.Data from exercise 4Request a frequency distribution and a histogram for the
In a negatively skewed distribution, are the unusual scores extremely large or extremely small? At what end of the graph is the “tail”?
Request a frequency distribution and a histogram for the variables Baseline Anxiety and Baseline Heart Rate for all students. Comment on your statistical software's choice of class intervals for each
Request a frequency distribution and a histogram for the variable Quiz Score across all students. Describe the shape of this distribution.
In a positively skewed distribution, are the unusual scores extremely large or extremely small? At what end of the graph is the “tail”?
What is a symmetric distribution?
For which of the following should you use a bar chart, and for which should you use a histogram? Why?(a) Scores on a midterm examination in psychology taken by 50 students.(b) The number of children
Request a frequency distribution and a bar chart for the variable Undergraduate Major across all 100 of Ihno's students.
What kind of measurement scales are used for each of the following variables in Ihno's study?(a) The gender of each student.(b) The undergraduate major of each student.(c) The number of math courses
A poll of sportswriters ranks the 25 best college football teams in the country, where #1 is the best team, #2 is the second best team, and so on. What kind of measurement scale is this?
Create a new variable that is 10 times the statistics quiz score. How does the sum of this variable compare to the sum of the original variable? What general rule is being illustrated by this
We are classifying psychiatric patients as having one or another of five different psychological disorders— Major Depressive Disorder, Bipolar Disorder, Generalized Anxiety Disorder,
Create a new variable that adds 10 points to everyone's math background quiz score. How does the sum of this variable compare to the sum of the original variable? What general rule is being
What important property do interval scales have that ordinal and nominal scales do not have?
Label the values of the categorical (i.e., qualitative) variables according to the following codes: For gender, 1 = Female and 2 = Male; for undergrad major, 1 = Psychology, 2 = Pre-med, 3 = Biology,
Calculate the mean deviation for Doty Hall, and compare it to σ (as calculated in Exercise 7). What do you think would happen to the difference of these two measures if you were to add an extreme
Express the following words in symbols.(a) Add up all the scores on test X, then add up all the scores on test Y, and then add the two sums together.(b) Add up all the scores on test G. To this, add
Compute the following (these values will not by themselves help Carrie to make a decision about the dormitories, but we will use these values as steps in future exercises to answer Carrie's
Five students are enrolled in an advanced course in psychology. Two quizzes are given early in the semester, each worth a total of 10 points. The results are as follows:(a) Compute each of the
For each of the following (separate) sets of data, compute the values needed in order to fill in the answer spaces. Then answer the additional questions that follow.(Use the appropriate summation
Compute the values needed to fill in the blanks. Data set 3: N =. γ ΣΧ= Σχ (Σχ)- ΣΧΥ- ΣΧ+Y )= 89 ΣΥ- ΣΥ2 (ΣΥ- ΣΧΣΥ ΣΧ-y) = 97 57 2 68 3 85 87 %3| 4 74 76 92 97 92 79 100 91 50
Create regular and cumulative frequency distributions for the data from the Turck, Kirk, and Dupre dormitories (see first exercise of Chapter 1).Data from first exerciseCompute the following (these
Create grouped and cumulative grouped frequency distributions for Turck and Kirk Halls.
Plot a histogram corresponding to the grouped frequency distribution that you created for Turck Hall in the previous exercise. What kind of distribution shape do you see?
Using the grouped frequency distributions you created for Turck and Kirk Halls in Exercise 2, plot the two corresponding frequency polygons on the same set of axes (i.e., in one graph).
Create a stem-and-leaf plot for the data from Turck Hall, using an interval size of 3.
Calculate the friendliness means of Turck, Kirk, Dupre, and Doty Halls (see first exercise of Chapter 1).Data from first exerciseCompute the following (these values will not by themselves help Carrie
Compute the median of Turck Hall from the regular frequency distribution you created for that dorm when solving the first exercise of Chapter 2.
Using the definitional formula, calculate the (biased) “variance” of Doty Hall in terms of deviations from the median, rather than the mean, of that distribution (just put the five scores in
Using the results you found for Exercise 9 in Chapter 2, compute the interquartile range and SIQR for Turck Hall. Using the same methods, calculate these measures for Kirk Hall, as well.
For each of the frequency distributions shown in the following table, state whether it isa. (approximately) normalb. Unimodal, skewed to the rightc. Unimodal, skewed to the leftd. Bimodal,
Use the regular (ungrouped) frequency distribution that you created for Turck Hall in Exercise 1 to solve this exercise.(a) Estimate the percentile rank corresponding to a score of 8.(b) Estimate the
Use the grouped frequency distribution that you created for Kirk Hall in Exercise 2 to solve this exercise.a. Estimate the percentile rank corresponding to a score of 16.b. Estimate the percentile
Use the same distribution for this exercise that you used for Exercise 7.a. Approximately what score corresponds to the 25th percentile?b. Approximately what score corresponds to the 75th percentile?
Use the same grouped distribution for this exercise that you used for Exercise 8.a. Estimate the score that corresponds to the second decile.b. Estimate the score that corresponds to the 50th
Find the mode of Kirk Hall by inspecting the regular frequency distribution you created for that dorm when solving the first exercise of Chapter 2.
Using the raw data for Dupre Hall, demonstrate that the sum of the deviations from the mean equals zero.
Compute the range for each of the four dorms.
Compute the biased and unbiased standard deviations for Distribution 6 in Table 3.2.Table 3.2 Distribution 3 6. 4 7.0 7.2 40.2 7.0 10.0 97.8 7.0 7.1 40.1 7.0 10.0 88.5 7.0 7.1 40.1 6.0 9.0 83.4 40.1
The mean of a set of scores is 8 and the standard deviation is 4. What will the new mean, standard deviation, and variance be if you:a. Add 6.8 to every number?b. Subtract 4 from every number?c.
For each of the following, compute the z score; then compute the T score.a. A Turck Hall student with a score of 17.b. A Turck Hall student with a score of 11.c. A Kirk Hall student with a score of
Consider the following data:This student believes that he has performed better on the psychology test for two reasons: His score is higher, and he is only 8 points below average (as opposed to 10
Which of each pair is better, or are they the same? (You should be able to answer by inspection.)a. A T score of 47 and a z score of + 0.33b. A T score of 64 and a z score of + 0.88c. A T score of 42
For data set 3 in Chapter 1 (reproduced here), transform each subject's (S) score on X to a z score. Then transform each subject's score on Y to a z score. х Zx Zy 97 89 2 57 68 3 85 87 4 74 76 92
Find the mean and standard deviation (σ) for the following data set:68.36, 15.31, 77.42, 84.00, 76.59, 68.43, 72.41, 83.05, 91.07, 80.62, 77.83Transform each raw score in the preceding data set into
What percent of the population obtains scores of 410 or less?
How do you explain the fact that the answer to Exercise 9 is smaller than the answer to Exercise 8, even though each problem deals with a 100-point range of scores?
What is the minimum score needed to rank in the top 5% of the population?
A psychology instructor develops a training method that is designed to improve the examination scores of poor students. The performance of a sample of 12 such students on the posttest (X1) following
a. Convert the data in part (a) of Exercise 3 to ranks, separately for each variable, in order to compute the Spearman rank-order correlation coefficient. Test rS for statistical significance by
Use the data and your results from Exercise 1 in Chapter 9 to compute the linear regression equation for predicting the sophomore average (Y) from the number of cuts (C). What sophomore average would
The following data come from Exercise 5 in Chapter 7. Calculate rpbfor these data by assigning an X value of 0 to Group 1 and an X value of 1 to Group 2. What proportion of the variance in the scores

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