Recall Exercise 1.2.16, in which researchers asked 40 heterosexual couples which person said “I love you first.”

They found that the man said “I love you” in 28 of the 40 couples before the woman did. Since previous research indicated that the man tends to say “I love you” before the woman, we tested to see if the probability a man would say “I love you” before the woman is more than 50%.
a. State the appropriate null and alternative hypotheses (in symbols) for testing whether males are more likely to say “I love you” first.
b. Using an appropriate applet, find the p-value using a theory-based test (one-proportion z-test; 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?
e. Without using an applet, determine the value of the theory-based (normal approximation) p-value if we used a two-sided alternative hypothesis.