Reconsider Exploration 1.3, where we explored whether the long-run proportion that students in a class would correctly assign the names Bob and Tim to the pictures. We tested to see if this long-run proportion is more than 0.50.
a. State the appropriate null and alternative hypotheses in the context of this study.
b. In a class of one of the authors 19 out of 30 students correctly identified that the face on the left belonged to Tim. Using an appropriate applet, find the p-value using a one-proportion z-test (theory-based/normal approximation).
c. Summarize your conclusion from your p-value.
d. What is the z-statistic for the test? What does this number represent in the context of this study?