1. A STAT instructor wants to compare the final exam scores of students taught using two different curricula. She obtains a sample of 600 students. She randomly assigns 300 students to a traditional curriculum and 300 students to a new curriculum. It is hypothesized that the new curriculum will lead to higher scores. If there is no significant difference, then she will continue to teach using the older curriculum. If there is a significant difference, then she will switch to the new curriculum.
A. State the null and alternative hypotheses that the instructor should test. Use m1to denote the mean final exam score of students in the traditional curriculum group and m2to denote the mean final exam score of students in the new curriculum group.
B. What does a Type I error mean in this situation? What are the consequences of making a Type I error here?
C. What does a Type II error mean in this situation? What are the consequences of making a Type II error here?
D. In this scenario, is a Type I or Type II error more serious? Or, are they equally serious? Explain your reasoning.
E. If you were working with this researcher, what alpha level would you use and why?
Assume that the instructor completes this study and finds m1=40 and m2=41 with a pooled standard deviation of 7. Her p-value is 0.0403.
F. Compute Cohen’s das a measure of effect size.
G. Using the alpha level you selected in part E, are her results statistically significant? Explain why or why not.
H. Are her results practically significant? Explain why or why not.
2. The manager of a restaurant wants to know if there is a correlation between the amount of a customer’s bill and the percent that they tip. In other words, as people spend more money do they tend to tip at different rates? With data from a random sample of 157 bills, he used StatKey to construct a 95% bootstrap confidence interval of [0.018, 0.292] for r. [24 points]
A. What if the manager wanted a hypothesis test instead? What would be the appropriate null and alternative hypotheses?
B. Based on the 95% confidence interval, would you expect the manager to reject or fail to reject the null hypothesis at the 0.05 alpha level? Explain your reasoning.
C.Using this scenario, compare and contrast confidence intervals and hypothesis testing. List at least one similarity and at least one difference.
3. A researcher wants to compare the means of 4 different groups. What procedure(s) should he use and why?