Researchers at Harris Interactive wondered if there was a difference between males and females in regard to some common annoyances. They asked a random sample of males and females, the following question: "Are you annoyed by people who repeatedly check their mobile phones while having an in-person conversation?" Among the 540 males surveyed, 178 responded "Yes"; among the 560 females surveyed, 206 responded "Yes." Does the evidence suggest a higher proportion of females are annoyed by this behavior?
(a) Explain why this study can be analyzed using the methods for conducting a hypothesis test regarding two independent proportions.
(b) What are the null and alternative hypotheses?
(c) Describe the sampling distribution of p̅female - p̅male. Draw a normal model with the area representing the P-value shaded for this hypothesis test.
(d) Determine the P-value based on the model from part (c).
(e) Interpret the P-value.
(f) Based on the P-value, what does the sample evidence suggest? That is, what is the conclusion of the hypothesis test? Assume an a = 0.05 level of significance.