# Chapter 11- even problems | Statistics homework help

**Chapter 11 Evens**

**6. a. **A repeated-measures study with a sample of *n *= 25 participants produces a mean difference of *MD* = 3 with a standard deviation of *s *= 4. Based on the mean and standard deviation, you should be able to visualize (or sketch) the sample distribution. Use a two-tailed hypothesis test with α = .05 to determine whether it is likely that this sample came from a population with μ*D* = 0.

**b. **Now assume that the sample standard deviation is *s *= 12, and once again visualize the sample distribution. Use a two-tailed hypothesis test with α =.05 to determine whether it is likely that this sample came from a population with μ*D* = 0.

**c**. Explain how the size of the sample standard deviation influences the likelihood of finding a significant mean difference.

**8. **A sample of difference scores from a repeated-measures experiment has a mean of *MD *= 4 with a standard deviation of *s*= 6.

**a. **If *n *= 4, is this sample sufficient to reject the null hypothesis using a two-tailed test with α =.05?

**b. **Would you reject *H*0 if *n *= 16? Again, assume a two-tailed test with α =.05.

**c. **Explain how the size of the sample influences the likelihood of finding a significant mean difference.

**10. **Research has shown that losing even one night’s sleep can have a significant effect on performance of complex tasks such as problem solving (Linde & Bergstroem, 1992). To demonstrate this phenomenon, a sample of *n *= 25 college students was given a problem-solving task at noon on one day and again at noon on the following day. The students were not permitted any sleep between the two tests. For each student, the difference between the first and second score was recorded. For this sample, the students averaged *MD* = 4.7 points better on the first test with a variance of *s*2 = 64 for the difference scores.

**a. **Do the data indicate a significant change in problem solving ability? Use a two-tailed test with α =.05.

**b. **Compute an estimated Cohen’s *d *to measure the size of the effect.

**12. **How would you react to doing much worse on an exam than you expected? There is some evidence to suggest that most individuals believe that they can cope with this kind of problem better than their fellow students (Igou, 2008). In the study, participants read a scenario of a negative event and were asked to use a 10-point scale to rate how it would affect their immediate well-being (-5 strongly worsen to +5 strongly improve). Then they were asked to imagine the event from the perspective of an ordinary fellow student and rate how it would affect that person. The difference between the two ratings was recorded. Suppose that a sample of *n *= 25 participants produced a mean difference of *MD* = 1.28 points (self rated higher) with a standard deviation of *s *= 1.50 for the difference scores.

**a. **Is this result sufficient to conclude that there is a significant difference in the ratings for self versus others? Use a two-tailed test with

α =.05.

**b. **Compute *r*2 and estimate Cohen’s *d *to measure the size of the treatment effect.

**c. **Write a sentence describing the outcome of the hypothesis test and the measure of effect size as it would appear in a research report.

**14. **Researchers have noted a decline in cognitive functioning as people age (Bartus, 1990). However, the results from other research suggest that the antioxidants in foods such as blueberries may reduce and even reverse these age-related declines (Joseph et al., 1999). To examine this phenomenon, suppose that a researcher obtains a sample of *n *= 16 adults who are between the ages of 65 and 75. The researcher uses a standardized test to measure cognitive performance for each individual. The participants then begin a 2-month program in which they receive daily doses of a blueberry supplement. At the end of the 2-month period, the researcher again measures cognitive performance for each participant. The results show an average increase in performance of *MD* = 7.4 with *SS *= 1215.

**a. **Does this result support the conclusion that the antioxidant supplement has a significant effect on cognitive performance? Use a two-tailed test with α =.05.

**b. **Construct a 95% confidence interval to estimate the average cognitive performance improvement for the population of older adults.

**16. **A researcher for a cereal company wanted to demonstrate the health benefits of eating oatmeal. A sample of 9 volunteers was obtained and each participant ate a fixed diet without any oatmeal for 30 days. At the end of the 30-day period, cholesterol was measured for each individual. Then the participants began a second 30-day period in which they repeated exactly the same diet except that they added 2 cups of oatmeal each day. After the second 30-day period, cholesterol levels were measured again and the researcher recorded the difference between the two scores for each participant. For this sample, cholesterol scores averaged *MD* = 16 points lower with the oatmeal diet with *SS *= 538 for

the difference scores.

**a. **Are the data sufficient to indicate a significant change in cholesterol level? Use a two-tailed test with α =.01.

**b. **Compute *r*2*, *the percentage of variance accounted for by the treatment, to measure the size of the treatment effect.

**c. **Write a sentence describing the outcome of the hypothesis test and the measure of effect size as it would appear in a research report.

**18. **One of the primary advantages of a repeated-measures design, compared to independent-measures, is that it reduces the overall variability by removing variance caused by individual differences. The following data are from a research study comparing two treatment conditions.

**a. **Assume that the data are from an independent measures study using two separate samples, each with *n *= 6 participants. Compute the pooled variance and the estimated standard error for the mean difference.

**b. **Now assume that the data are from a repeated measures study using the same sample of *n *= 6 participants in both treatment conditions. Compute the variance for the sample of difference scores and the estimated standard error for the mean difference. (You should find that the repeated measures design substantially reduces the variance and the standard error.)

Treatment 1 Treatment 2 Difference

10 13 3

12 12 0

8 10 2

6 10 4

5 6 1

7 9 2

*M *= 8 *M *= 10 *MD* = 2

*SS *= 34 *SS *= 30 *SS *= 10

**20. **A researcher uses a matched-subjects design to investigate whether single people who own pets are generally happier than singles without pets. A mood inventory questionnaire is administered to a group of 20- to 29-year-old non–pet owners and a similar age group of pet owners. The pet owners are matched one to one with the non–pet owners for income, number of close friendships, and general health. The data are as follows:

Matched Non–Pet Pet

Pair Owner Owner

A 12 14

B 8 7

C 10 13

D 9 9

E 7 13

F 10 12

**a. **Is there a significant difference in the mood scores for non–pet owners versus pet owners? Test with α = .05 for two tails.

**b. **Construct the 95% confidence interval to estimate the size of the mean difference in mood between the population of pet owners and the population of non–pet owners. (You should find that a mean difference of µ*D* = 0 is an acceptable value, which is consistent with the conclusion from the hypothesis test.)

**22. **The teacher from the previous problem also tried a different approach to answering the question of whether changing answers helps or hurts exam grades. In a separate class, students were encouraged to review their final exams and change any answers they wanted to before turning in their papers. However, the students had to indicate both the original answer and the changed answer for each question. The teacher then graded each exam twice, one using the set of original answers and once with the changes. In the class of *n *= 22 students, the average exam score improved by an average of *MD* = 2.5 points with the changed answers. The standard deviation for the difference scores was *s *= 3.1. Are the data sufficient to conclude that rethinking and changing answers can significantly improve exam scores? Use a one-tailed test at the .01 level of significance.

**24. **The Preview section of this chapter presented a repeated-measures research study demonstrating that swearing can help reduce pain (Stephens, Atkins, & Kingston, 2009). In the study, each participant was asked to plunge a hand into icy water and keep it there as long as the pain would allow. In one condition, the participants repeated their favorite curse words while their hands were in the water. In the other condition, the participants repeated a neutral word. Data similar to the results obtained in the study are shown in the following table.

**a. **Do these data indicate a significant difference in pain tolerance between the two conditions? Use a two-tailed test with α = .05.

**b. **Compute *r*2, the percentage of variance accounted for, to measure the size of the treatment effect.

**c. **Write a sentence demonstrating how the results of the hypothesis test and the measure of effect size would appear in a research report.

Amount of Time (in Seconds)

Participant Swear Words Neutral Words

1 94 59

2 70 61

3 52 47

4 83 60

5 46 35

6 117 92

7 69 53

8 39 30

9 51 56

10 73 61