2. The value of the z-score in a hypothesis test is influenced by a variety of factors. Assuming that all other variables are held constant, explain how the value of z is influenced by each of the following:
a. Increasing the difference between the sample mean and the original population mean.
b. Increasing the population standard deviation.
c. Increasing the number of scores in the sample.
4. If the alpha level is changed from a = .05 to a = .01:
a. What happens to the boundaries for the critical region?
B. What happens to the probability of a Type I error?
6. 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 µ = 40 and a standard deviation of σ = 12. The sample of group-participation adolescents had an average of M = 43.84.
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 a = .01.
b. Compare Cohen’s d to measure the size of the difference.
c. Write a sentence describing the outcome of the hypothesis test and the measurement of effect size as it would appear in a research report.
8. A random sample is selected from a normal population with a mean of µ = 50 and a standard deviation of σ = 12. After a treatment is administered to the individuals in the sample, the sample mean is found to be M = 55.
a. If the sample consists of n = 16 scores, is the sample mean sufficient to conclude that the treatment has a significant effect? Use a two-tailed test with a = .05.
b. If the sample consists of n = 36 scores, is the sample mean sufficient to conclude that the treatment has a significant effect? Use a two-tailed test with a = .05.
c. Comparing your answers for parts a and b, explain how the size of the sample influences the outcome of a hypothesis test.
12. There is some evidence that REM sleep, associated with dreaming, may also play a role in learning and memory processing. For example, Smith and Lapp (1991) found increased REM activity for college students during exam periods. Suppose that REM activity for a sample of n = 16 students during the final exam period produced an average score of M = 143. Regular REM activity for the college population averages µ = 110 with a standard deviation of σ =50. The population distribution is approximately normal.
a. Do the data from the sample provide evidence for a significant increase in REM activity during exams? Use a one-tailed test with a = .01.
b. Compare Cohen’s d to estimate the size of the effect.
c. Write a sentence describing the outcome of the hypothesis test and the measure of effect size as it would appear in research report.
18. A researcher plans to conduct an experiment testing the effect of caffeine on reaction time during a driving simulation task. A sample of n = 9 participants is selected and each person receives a standard dose of caffeine before being tested on the simulator. The caffeine is expected to lower reaction time by an average of 30 msec. Scores on the simulator task for the regular population (without caffeine) form a normal distribution with µ = 240 msec. and σ = 30.
a. If the researcher uses a two-tailed test with a = .05, what is the power of the hypothesis test?
b. Again assuming a two-tailed test with a = .05, what is the power of the hypothesis test if the sample size is increased to n = 25?
20. Briefly explain how increasing sample size influences each of the following. Assume that all other factors are held constant.
a. The size of the z-score in a hypothesis test.
b. The size of Cohen’s d.
c. The power of the hypothesis test.
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