Hypothesis Testing, Cohen's d & Power

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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 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. 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 of the year. For the regular population of third-grade children, scores on the test form a normal distribution with a mean of m = 150 and a standard deviation of SD = 25. The mean for the sample is M = 158
a. Identify the independent and the dependent variable for this study.
b. Assuming a two-tailed test stated the null hypothesis in a sentence than includes the independent variable and the dependent variable.
c. Using symbols stated the hypotheses (Ho and H1) for the two-tailed test.
d. Sketch the appropriate distribution, and locate the critical region for p = .05.
e. Calculate the test statistic (z-scores) for the sample.
f. What decision should be made about the null hypothesis, and what decision should be made 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 is obtained and the students are place in the course during their first semester. One yea later, a writing sample is obtained for each student and the writing samples are graded using a standardized evaluation technique. The average score for the same is M = 76. For the general population of college students, writing scores form a normal distribution with a mean of m = 70.
A. If the writing scores for the population have standard deviation of σ = 20, does the sample provide enough evidence to conclude that the new composition course has a significant effect? Assume a two-tailed test with p = .05.
B. If the population standard deviation is SD = 10, is the sample sufficient to demonstrate a significant effect? Again, assume a two-tailed test with p = .05.
c. Briefly explain why you reached different conclusion for part a and b.

18. A sample on n = 16 individuals is selected from a normal population with a mean of m = 48 and a standard deviation SD = 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 effect.
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 the population standard deviation were SD = 24, what value would be obtained for Cohen's d? How does 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 the mean difference influence the measure of effect size?

22. Explain how the power of a hypothesis test this influenced by each of the following. Assume that all other factors are held constant.
a. Increasing the alpha level from .01 to .05.
b. changing from a one-tailed test to a two tailed test.

24. A researcher is evaluating the influence of treatment using a sample selected from a normally distributed population with a mean of M = 80 and a standard deviation of SD; = 20. The researcher expects a 12-point treatment effect and plan to use a two-tailed hypothesis test with p= .05.
a. Compute the power of the test if the researcher use a sample of n = 16 individuals.
b. Compute the power of the test if the researcher uses a sample of n = 25 individuals.