12. Childhood participation in sports, cultural groups, and youth groups appears to be related to improved self-esteem for adolescents (McGee, Williams, Howden-Chapman, Martin, & Kawachi, 2006). In a representative study, a sample of n = 100 adolescents with a history of group participation is given a standardized self-esteem questionnaire. For the general population of adolescents, scores on this questionnaire form a normal distribution with a mean of = 50 and a standard deviation of = 15. The sample of group-participation adolescents had an average of M = 53.8.

a. Does this sample provide enough evidence to conclude that self-esteem scores for these adolescents are significantly different from those of the general population? Use a two-tailed test with = .05.

The null hypothesis is H: , even group participation.

The standard error is (50, 15, 53.8, 1.5) , so z = (to two decimal places). Using the Distributions tool, the critical value of z = .

Is there a significant effect?

No

Yes

b. Compute Cohen's d to measure the size of the difference.

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.

The results indicate that (group participation, adolescence, self-esteem) (has a significant, does not have an, has an insignificant) effect on (self-esteem, group participation, adolescence) : z (>2.53, <0.05, =2.53), p (<0.05, >2.53, =0.25), d (>2.53, =0.25, <0.05.

16. Researchers at a weather center in the northeastern United States recorded the number of 90 Fahrenheit days each year since records first started in 1875. The numbers form a normal-shaped distribution with a mean of = 9.6 and a standard deviation of = 1.9. To see if the data showed any evidence of global warming, they also computed the mean number of 90 days for the most recent n = 4 years and obtained M = 12.25. Do the data indicate that the past four years have had significantly more 90 days than would be expected for a random sample from this population? Use a one-tailed test with = .05.

The standard error is , and the sample mean corresponds to z = . (Round your answer to two decimal places.) This is well beyond the critical boundary of (2.33, 1.64, 1.96). (Do not reject, Reject) the null hypothesis, and conclude that the past 4 years (constitute, do not constitute) a representative sample from a population with a mean of = 9.6.

24. Explain how the power of a hypothesis test is influenced by each of the following. Assume that all other factors are held constant.

Increasing the alpha level from .01 to .05 (increases, does not affect, decreases) the power of a hypothesis test.

Changing from a one-tailed test to a two-tailed test (does not affect, decreases, increases) the power of a hypothesis test.

Increasing effect size (increases, does not affect, decreases)the power of a hypothesis test.