**Chapter 10: Evens**

**2. **Describe what is measured by the estimated standard error in the bottom of the independent-measures *t *statistic.

**4. **Describe the homogeneity of variance assumption and explain why it is important for the independent measures *t *test.

**6. **One sample has *SS *= 70 and a second sample has *SS *= 42.

**a. **If *n *= 8 for both samples, find each of the sample variances, and calculate the pooled variance. Because the samples are the same size, you should find that the pooled variance is exactly halfway between the two sample variances.

**b. **Now assume that *n *= 8 for the first sample and *n *= 4 for the second. Again, calculate the two sample variances and the pooled variance. You should find that the pooled variance is closer to the variance for the larger sample.

**8. **Two separate samples, each with *n *_ 12 individuals, receive two different treatments. After treatment, the first sample has *SS *= 1740 and the second has *SS *= 1560.

**a. **Find the pooled variance for the two samples.

**b. **Compute the estimated standard error for the sample mean difference.

**c. **If the sample mean difference is 8 points, is this enough to reject the null hypothesis and conclude that there is a significant difference for a two-tailed test at the .05 level?

**d. **If the sample mean difference is 12 points, is this enough to indicate a significant difference for a two-tailed test at the .05 level?

**e. **Calculate the percentage of variance accounted for (*r*2) to measure the effect size for an 8-point mean difference and for a 12-point mean difference.

**10. **For each of the following, assume that the two samples are selected from populations with equal means and calculate how much difference should be expected, on average, between the two sample means.

**a. **Each sample has *n *= 5 scores with *s*2 = 38 for the first sample and *s*2 = 42 for the second. (*Note: *Because the two samples are the same size, the pooled variance is equal to the average of the two sample variances.)

**b. **Each sample has *n *= 20 scores with *s2* = 38 for the first sample and *s2* = 42 for the second.

**c. **In part b, the two samples are bigger than in part a, but the variances are unchanged. How does sample size affect the size of the standard error for the sample mean difference?

**12. **A researcher conducts an independent-measures study comparing two treatments and reports the *t *statistic as *t*(30) = 2.085.

**a. **How many individuals participated in the entire study?

**b. **Using a two-tailed test with α=.05, is there a significant difference between the two treatments?

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

**14. **Do you view a chocolate bar as delicious or as fattening? Your attitude may depend on your gender. In a study of American college students, Rozin, Bauer, and Catanese (2003) examined the importance of food as a source of pleasure versus concerns about food

associated with weight gain and health. The following results are similar to those obtained in the study. The scores are a measure of concern about the negative aspects of eating.

Males Females

*n *= 9 *n *= 15

*M *= 33 *M *= 42

*SS *= 740 *SS *= 1240

**a. **Based on these results, is there a significant difference between the attitudes for males and for females? Use a two-tailed test with α=. .05.

**b. **Compute *r*2, the percentage of variance accounted for by the gender difference, to measure effect size for this study.

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

**16. **Functional foods are those containing nutritional supplements in addition to natural nutrients. Examples include orange juice with calcium and eggs with omega-3. Kolodinsky, et al. (2008) examined attitudes toward functional foods for college students. For American students, the results indicated that females had a more positive attitude toward functional foods and were more likely to purchase them compared to

males. In a similar study, a researcher asked students to rate their general attitude toward functional foods on a 7-point scale (higher score is more positive). The results are as follows:

Females Male

*n *= 8 *n *= 12

*M *= 4.69 *M *= 4.43

*SS *= 1.60 *SS *= 2.72

**a. **Do the data indicate a significant difference in attitude for males and females? Use a two-tailed test with α=.05.

**b. **Compute *r*2, the amount of variance accounted for by the gender difference, to measure effect size.

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

**18. **Numerous studies have found that males report higher self-esteem than females, especially for adolescents (Kling, Hyde, Showers, & Buswell, 1999). Typical results show a mean self-esteem score of *M *= 39.0 with *SS *= 60.2 for a sample of *n *= 10 male adolescents and a mean of *M *= 35.4 with *SS *= 69.4 for a sample of *n *= 10 female adolescents.

**a. **Do the results indicate that self-esteem is significantly higher for males? Use a one-tailed test with α=.01.

**b. **Use the data to make a 95% confidence interval estimate of the mean difference in self-esteem between male and female adolescents.

**c. **Write a sentence demonstrating how the results from the hypothesis test and the confidence interval would appear in a research report.

**20. **When people learn a new task, their performance usually improves when they are tested the next day,

but only if they get at least 6 hours of sleep (Stickgold, Whidbee, Schirmer, Patel, & Hobson, 2000). The following data demonstrate this phenomenon. The participants learned a visual discrimination task on one day, and then were tested on the task the following

day. Half of the participants were allowed to have at least 6 hours of sleep and the other half were kept awake all night. Is there a significant difference between the two conditions? Use a two-tailed test with α = .05.

Performance Scores

6 Hours of Sleep No Sleep

*n *= 14 *n *= 14

*M *= 72 *M *= 65

*SS *= 932 *SS *= 706

**22. **Downs and Abwender (2002) evaluated soccer players and swimmers to determine whether the routine blows to the head experienced by soccer players produced long-term neurological deficits. In the study, neurological tests were administered to mature soccer players and swimmers and the results indicated significant differences. In a similar study, a researcher obtained the following data.

Swimmers Soccer players

10 7

8 4

7 9

9 3

13 7

7

6

12

**a. **Are the neurological test scores significantly lower for the soccer players than for the swimmers in the control group? Use a one-tailed test with α=.05.

**b. **Compute the value of *r*2 (percentage of variance accounted for) for these data.