Question 10.1

Question 10.2

Question 10.3

Question 10.4

Question 10.5

Question 10.6

Question 10.7

Question 10.8

Question 10.9

Question 10.10

Question 10.11

Question 10.12

Question 10.13

Question 10.14

Question 10.15

Identify critical t values for each of the following tests:

1. A one-tailed, paired-samples t test performed on before-and-after scores on the Marital Satisfaction Inventory for 18 people who went through marriage counseling, using a p level of 0.01.

2. A two-tailed, paired-samples t test performed on before-and-after scores on the Marital Satisfaction Inventory for 64 people who went through marriage counseling, using a p level of 0.05.

Question 10.16

Assume 8 participants completed a mood scale before and after watching a funny video clip.

1. Identify the critical t value for a one-tailed, paired-samples t test with a p level of 0.01.

2. Identify the critical t values for a two-tailed, paired-samples t test with a p level of 0.01.

Question 10.17

The following are scores for 8 students on two different exams.

1. Calculate the paired-samples t statistic for these exam scores.

2. Using a two-tailed test and a p level of 0.05, identify the critical t values and make a decision regarding the null hypothesis.

3. Assume you instead collected exam scores from 1000 students whose mean difference score and standard deviation were exactly the same as for these 8 students. Using a two-tailed test and a p level of 0.05, identify the critical t values and make a decision regarding the null hypothesis.

4. How did changing the sample size affect the decision regarding the null hypothesis?

Question 10.18

The following are mood scores for 12 participants before and after watching a funny video clip (higher values indicate better mood).

1. Calculate the paired-samples t statistic for these mood scores.

2. Using a one-tailed hypothesis test that the video clip improves mood, and a p level of 0.05, identify the critical t values and make a decision regarding the null hypothesis.

3. Using a two-tailed hypothesis test with a p level of 0.05, identify the critical t values and make a decision regarding the null hypothesis.

Question 10.19

Consider the following data:

1. Calculate the paired-samples t statistic, assuming a two-tailed test.

2. Calculate the 95% confidence interval, assuming a two-tailed test.

3. Calculate the effect size for the mean difference.

Question 10.20

Consider the following data.

1. Calculate the paired-samples t statistic, assuming a two-tailed test.

2. Calculate the 95% confidence interval.

3. Calculate the effect size.

Question 10.21

Assume we know the following for a paired-samples t test: N = 13, M_difference = −0.77, s = 1.42.

1. Calculate the t statistic.

2. Calculate a 95% confidence interval for a two-tailed test.

3. Calculate effect size using Cohen’s d.

Question 10.22

Assume we know the following for a paired-samples t test: N = 32, M_difference = 1.75, s = 4.0.

1. Calculate the t statistic.

2. Calculate a 95% confidence interval for a two-tailed test.

3. Calculate the effect size, using Cohen’s d.

Question 10.23

Question 10.24

t tests and retail: Many communities worldwide are lamenting the effects of so-called big box retailers (e.g., Walmart) on their local economies, particularly on small, independently owned shops. Do these large stores affect the bottom lines of locally owned retailers? Imagine that you decide to test this premise. You assess earnings at 20 local stores for the month of October, a few months before a big box store opens. You then assess earnings the following October, correcting for inflation.

1. What are the two populations?

2. What is the comparison distribution? Explain.

3. Which hypothesis test would you use? Explain.

4. Check the assumptions for this hypothesis test.

5. What is one flaw in drawing conclusions from this comparison over time?

6. State the null and research hypotheses in both words and symbols.

Question 10.25

Paired-samples t tests, confidence intervals, and hockey goals: Below are the numbers of goals scored by the lead scorers of the New Jersey Devils hockey team in the 2007–2008 and 2008–2009 seasons. On average, did the Devils play any differently in 2008–2009 than they did in 2007–2008?

1. Conduct the six steps of hypothesis testing using a two-tailed test and a p level of 0.05.

2. Report the test statistic in APA format.

   259

3. Calculate the confidence interval for the paired-samples t test you conducted in part (a). Compare the confidence interval to the results of the hypothesis test.

4. Calculate the effect size for the mean difference between the 2007–2008 and 2008–2009 seasons.

Question 10.26

Paired-samples t test and graduate admissions: Is it harder to get into graduate programs in psychology or history? We randomly selected five institutions from among all U.S. institutions with graduate programs. The first number for each is the minimum grade point average (GPA) for applicants to the psychology doctoral program, and the second is for applicants to the history doctoral program. These GPAs were posted on the Web site of the well-known college guide company Peterson’s.

• Wayne State University: 3.0, 2.75

• University of Iowa: 3.0, 3.0

• University of Nevada, Reno: 3.0, 2.75

• George Washington University: 3.0, 3.0

• University of Wyoming: 3.0, 3.0

1. The participants are not people; explain why it is appropriate to use a paired-samples t test for this situation.

2. Conduct all six steps of a paired-samples t test. Be sure to label all six steps.

3. Calculate the effect size and explain what this adds to your analysis.

4. Report the statistics as you would in a journal article.

Question 10.27

Attitudes toward statistics and the paired-samples t test: A professor wanted to know if her students’ attitudes toward statistics changed by the end of the course, so she asked them to fill out an “Attitudes Toward Statistics” scale at the beginning of the term and at the end of the term.

1. What kind of t test should she use to analyze the data?

2. If the average (mean) at the end of the class was higher than it was at the beginning, is that necessarily a statistically significant improvement?

3. Which situation makes it easier to declare that a certain mean difference is statistically significant: a class with 7 students or a class with 700 students? Explain your answer.

Question 10.28

Paired-samples t tests, confidence intervals, and wedding-day weight loss: It seems that 14% of engaged women buy a wedding dress at least one size smaller than their current size. Why? Cornell researchers reported an alarming tendency for women who are engaged to sometimes attempt to lose an unhealthy amount of weight prior to their wedding (Neighbors & Sobal, 2008). The researchers found that engaged women weighed, on average, 152.1 pounds. The average ideal wedding weight reported by 227 women was 136.0 pounds. The data below represent the fictional weights of 8 women on the day they bought their wedding dress and on the day they got married. Did women lose weight for their wedding day?

1. Conduct the six steps of hypothesis testing using a one-tailed test and a p level of 0.05.

2. Report the test statistic in APA format.

3. Calculate the confidence interval for the paired-samples t test that you conducted in part (a). Compare the confidence interval to the results of the hypothesis test.

Question 10.29

Hypnosis and the Stroop effect: In Chapter 1, you were given an opportunity to complete the Stroop test, in which color words are printed in the wrong color; for example, the word red might be printed in the color blue. The conflict that arises when we try to name the color of ink the words are printed in but are distracted when the color word does not match the ink color increases reaction time and decreases accuracy. Several researchers have suggested that the Stroop effect can be decreased by hypnosis. Raz, Fan, and Posner (2005) used brain-imaging techniques to demonstrate that posthypnotic suggestion led highly hypnotizable people to see Stroop words as nonsense words. Imagine that you are working with Raz and colleagues and your assignment is to determine whether reaction times decrease (remember, a decrease is a good thing; it indicates that participants are faster) when highly hypnotizable people receive a posthypnotic suggestion to view the words as nonsensical. You conduct the experiment on six participants, once in each condition, and receive the following data; the first number is reaction time in seconds without the posthypnotic suggestion, and the second number is reaction time with the posthypnotic suggestion:

• Participant 1: 12.6, 8.5

• Participant 2: 13.8, 9.6

• Participant 3: 11.6, 10.0

• Participant 4: 12.2, 9.2

• Participant 5: 12.1, 8.9

• Participant 6: 13.0, 10.8

1. What is the independent variable and what are its levels? What is the dependent variable?

2. Conduct all six steps of a paired-samples t test as a two-tailed test. Be sure to label all six steps.

3. Report the statistics as you would in a journal article.

4. Now let’s look at the effect of switching to a one-tailed test. Conduct steps 2, 4, and 6 of hypothesis testing for a one-tailed paired-samples t test. Under which circumstance—a one-tailed or a two-tailed test—is it easier to reject the null hypothesis? If it becomes easier to reject the null hypothesis under one type of test (one-tailed versus two-tailed), does this mean that there is a bigger mean difference between the samples? Explain.

5. Now let’s look at the effect of p level. Conduct steps 4 and 6 of hypothesis testing for a p level of 0.01 and a two-tailed test. With which p level—0.05 or 0.01—is it easiest to reject the null hypothesis with a two-tailed test? If it is easier to reject the null hypothesis with certain p levels, does this mean that there is a bigger mean difference between the samples? Explain.

6. Now let’s look at the effect of sample size. Calculate the test statistic using only participants 1–3 and determine the new critical values. Is this test statistic closer to or farther from the cutoff? Does reducing the sample size make it easier or more difficult to reject the null hypothesis? Explain.

7. How might order effects influence the results of this study?

8. Could the researchers use a counterbalanced design? Why or why not? What might they do instead if they think order effects are a problem?

Question 10.30

Political bias in academia and a paired-samples t test: The following is an excerpt from the abstract (brief opening summary) from a published research study examining a reported bias against conservatives in American academia (Fosse, Gross, & Ma, 2011).

The American professoriate contains a disproportionate number of people with liberal political views. Is this because of political bias or discrimination?…We sent two emails to directors of graduate study in the leading American departments of sociology, political science, economics, history, and English. The emails came from fictitious students who expressed interest in doing graduate work in the department…We analyze responses received in terms of frequency, timing, amount of information provided about the department, emotional warmth, and enthusiasm toward the student. (p. 1)

One of the fictional emails was from a fictional student who mentioned working on the presidential campaign of John McCain, a well-known conservative, and one was from a fictional student who mentioned working on the presidential campaign of Barack Obama, a well-known liberal. The researchers conducted a series of paired-samples t tests, but did not find statistically significant differences on the various measures between the conservative and liberal students.

1. Why is this a within-groups design?

2. What is the independent variable and what are its levels?

3. What are the dependent variables, as listed in the study description, and what kind of variables are they?

4. Explain why it would have been possible to conduct a paired-samples t test.

5. Explain why there may have been order effects in this study.

6. How might the researchers have used counterbalancing?

7. Was the p value likely to be lower than or higher than 0.05? Explain your answer.

8. Given that the results were not statistically significant, what additional information would you want to know to determine whether there was sufficient statistical power?