In a Gallup Youth Survey done in 2000, n = 501 randomly selected American teenagers were asked about how well they get along with their parents.
a. According to the Gallup Organization, the margin of error for the poll was 5%. Show how you think they determined this figure.
b. A survey result was that 54% of the sample said they get along "very well" with their parents. Using the reported margin of error, calculate a 95% confidence interval for the population proportion that gets along "very well" with their parents. Write a sentence that interprets this interval.
c. Using the more precise formula for margin of error given on page 383, calculate a 95% confidence interval. Compare the answer to the answer in part (b).
d. Another result in the same survey was that only 5% said that cheating on exams was "not at all serious." Using the reported margin of error, compute a 95% confidence interval for the population proportion who would say this. Also, compute the 95% confidence interval using the more precise formula for margin of error. Which interval is narrower?
e. You should have found that the intervals in parts (b) and (c) were quite similar to each other but that the two intervals computed in part (d) were not. Explain why the two intervals agreed more closely in parts (b) and (c) than they did in part (d).