A professor is investigating dominant themes in children’s picture books. She wants to know if themes differ depending on the gender of the main character.

After obtaining lists of all top-selling children’s picture books with a girl or boy protagonist over the last thirty years, she draws two random samples of fifty books, one sample with boy protagonists and the other with girl protagonists. Her undergraduate research assistants rate all one hundred books according to several themes, including

“emphasis on appearance,” which is measured on a scale ranging from 0 (no mention of physical appearance) to 50 (very strong emphasis on physical appearance). The professor asks her research team to use a two-sample test to compare emphasis on physical appearance by protagonists’ gender.

a. What is the dependent variable? What is the independent variable?

b. Would you recommend that the team conduct a one- or two-tailed test?

Explain why you would make this recommendation.

c. The team decides to set up a two-tailed hypothesis test. State the null and alternative hypotheses, in both words and statistical notation.

d. Assuming that the alpha-level is set at .01, sketch a t-distribution and label the following components: (1) the middle of the sampling distribution, (2)

decision t, and (3) p-value.

e. Which components of the t-distribution would differ from the one you sketched for Part d if this were a one-sample test, and why?