18. A sample of n=16 individuals is selected from a normal population with a mean of µ=48 and a standard deviation of ±=12. After receiving a treatment, the sample mean is found to be M = 52.
a. Compare 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 ±= 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 the 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 .01 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 form a normal distribution population with a mean u =8and a standard deviation of ±= 20. The researchers expects 12-point treatment effect and plans to use a two-tailed hypothesis test with ±= .05 .
a. Compute the power of the test if the researcher uses a sample of n = 16 individuals.
b. Compare the power of the test if the researcher uses a sample of n= 25 individuals.
The solution provides step by step method for the calculation of Cohen's d and power of a hypothesis test. Formula for the calculation and Interpretations of the results are also included.