Chapter 13, Problem 6E

How’s life? Gallup regularly conducts a poll using a “Cantril scale,” which asks respondents to imagine a ladder with 10 rungs. Rung 0 represents the worst possible life, and rung 10 represents the best possible life. Respondents are asked what rung they would say they are on. Responses are classified as “Thriving” (standing on rung 7 or higher, and expecting to be on rung 8 or higher five years from now), “Suffering” (standing on rung 4 or lower and expecting to be on rung 4 or lower five years from now), or “Struggling” (not thriving or suffering). In the first half of 2016, Gallup found that the index had reached a new high of 55.7% thriving with a sample size of 105,000. (www.gallup.com/ poll/194816/americans-life-evaluations-improve-during-obama-era.aspx)

1. a) Explain the meaning of $\hat{p}$ = 0.557 in the context of this situation.
2. b) Calculate the standard error of $\hat{p}$.
3. c) Explain what this standard error means in the context of this situation.