1.A researcher plans a study in which a crucial step is offering participants a food reward. It is important that the three food rewards be equal in appeal. Thus, a prestudy was designed in which participants were asked which of the rewards they preferred. Of the 60 participants, 16 preferred cupcakes, 26 preferred candy bars, and 18 favored dried apricots. Do these scores suggest that the different foods are differentially preferred by people in general? (Use the .05 significance level.)
a. Use the five steps of hypothesis testing.
b. Sketch the distribution involved.
c. Explain your findings.
2.A high school principal wanted to know if the racial makeup of her teachers mirrored that of the student body. The student body broke down into 47% White, 28% Latino, 15% African American, and 10% other. Of the 65 teachers, 42 were White, 4 were Latino, 15 were African American, and 4 were Other. Do these results suggest that the racial makeup of the faculty members is different from that of the students? (Use the .05 significance level.) Use the five steps of hypothesis testing and explain your findings.
3.Please make up and discuss research examples corresponding to the various techniques introduced throughout this course. Describe a plausible study for each of the following statistical procedures, indicating how it would apply and what results you would predict. Also include information about the number of participants you would assess and how you would go about estimating effect size and statistical power (when relevant).
a. correlation
b. multiple regression
c. t test for independent means
d. t test for dependent means
e. ANOVA
f. chi square for goodness of fit
g. chisquare test for independence