explain how you calculate the F-ratio, and explain why it is used in ANOVA.

INSTRUCTIONS TO CANDIDATES

ANSWER ALL QUESTIONS

Question 1 (18 points)

Briefly and concisely discuss in your own words the following:

A. Define the t statistic and the z-score. Why would you choose one over the

other? (Give at least two reasons.) (3 pts)

B. Compare Cohen’s d and r 2. When and why are they used? (3 pts)

C. Compare the independent-measures t test with the repeated measures t

test. Give an example of each. (3 pts)

D. Explain how to determine the Fcrit value using Table B.4, “The F

Distribution”, in Appendix B of your textbook. (3 pts)

E. Explain how you calculate the F-ratio, and explain why it is used in

ANOVA. (3 pts)

F. Compare the mean squares between treatments with the mean squares

within the treatment. Be sure to include the role of the treatment in each

mean square. (3 pts)

Question 2 (12 points)

A random sample of n = 30 has a mean of M = 56. Test the Ho that the population mean

is µ = 50 in situations a and b below.

A. The sample variance is s2 = 6: Use two-tailed test at α .05. Would the

t-statistic be significant? Show the five steps of hypothesis testing. (7 pts)

B. Suppose the sample variance is s2 = 300: Use two-tailed test at α .05.

Would the t-statistic be significant? (Show only Steps 3 and 4 of

hypothesis testing.) (3 pts)

C. Explain the effect of the size of the variance on the decisions you made

above. (2 pts)

Question 3 (16 points)

Given a sample of female students, n = 10, with SS = 600, and a sample of male

students, n = 12, with SS = 700:

A. Compute the pooled variance when you combine the two samples. (3 pts)

B. For the combined samples, what is the estimated standard error for the

sample mean difference? (3 pts)

C. If you computed the difference between the means of the two samples

and obtained a difference of 6, is this enough to reject the Ho for an

independent-measures hypothesis test using α .01, one-tailed test? (3

pts)

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