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# Hypothesis Testing, Power of Hypothesis Testing & Cohen's d

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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 of the sample.

4. If the alpha level is changed from ? = .05 to ? = .01.

a. What happens to the boundaries for the critical region?

b. What happens to the probability of a Type 1 error?

6. A researcher is investigating the effectiveness of a new study skills training program for elementary school children. A sample of n = 25 third grade children is selected to participate in the program and each child is given a standardized achievement test at the end the year. For the regular population of third grade children, scores on the test form a normal distribution with a mean of µ= 150 and standard deviation of Ï? = 25. The mean for the sample is M = 158.

a. Indenify the independent and the dependent variables for this study.

b. Assuming a two-tailed test, state the null hypothesis in a sentence that includes the independent variable and the dependent variable.

c. Using symbols, state the hypothesis (Ho and H1) for the two-tailed test.

d. Sketch the appropriate distribution, and locate the critical region for ? = .05

e. Calculate the test statistic (z-score) for the sample.

f. What decision should be made about the null hypothesis, and what decision should be about the effect of the program?

10. State College is evaluating a new English composition course for freshmen. A random sample of n = 25 freshmen. A random sample of n =25 freshmen is obtained and the students are placed in the course during their first semester. One year later, writing samples are graded using a standardized evaluation technique. The average score for the sample is M = 76. For the general population of college students, writing scores form a normal distribution with a mean of µ =70.

a. If the writing scores of the population have a standard deviation of Ï? =20, does the sample provide enough evidence to conclude that the new composition course has a significant effect? Assume a two-tailed test with ? = .05.

b. If the population standard deviation is Ï? = 10, is the sample sufficient to demonstrate a significant effect. Again, assume a two-tailed test with ? = .05.

c. Briefly, explain why reached different conclusion for part (a) and part (b).

18. A sample of n = 16 individuals is selected from a normal population with the mean of µ = 48 and the standard deviation of Ï? = 12. After receiving a treatment, the sample mean is found to be M = 52.

a. Compute Cohen's d to evaluate the size of the treatment plan.

b. If the sample size were n = 36, what value would be obtained for Cohen's d? How does sample size influence the measure of effect size?

c. If population standard deviation were Ï? =24 what value would be obtained for Cohen's d? How does the standard deviation influence the measure of effect size?

d. If the sample mean were M =56, what value would be obtained for Cohen's d? How does the size of the mean difference influence the measure of effect size?

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

a. Increasing the alpha level from .0.1 to .05.

b. Changing from a one-tailed test to a two-tailed test.

24. A researcher is evaluating the influence of a treatment using a sample selected from a normally distributed population with a mean of µ =80 and a standard deviation of Ï? = 20. He researcher expects a 12- point treatment effect and plans to use a two-tailed hypothesis test with ? = .05.

a. Compute the power of test if the researcher uses a sample of n =16 individuals.

b. Compute the power of the test if the researcher uses a sample of n = 25 individuals.