22 You Explain It Superstition A USA TodayGallup poll asked

22. You Explain It! Superstition: A USA Today/Gallup poll asked 1,006 adult Americans how much it would bother them to stay in a room on the 13th oor of a hotel. Interestingly, 13% said it would bother them. The margin of error was 3 percentage points with 95% condence. Which of the following represents a reasonable interpretation of the survey results? For those not reasonable, explain the aw.

(a) We are 95% condent that the proportion of adult Americans who would be bothered to stay in a room on the 13th oor is between 0.10 and 0.16.

Answer:

(b) We are between 92% and 98% condent that 13% of adult Americans would be bothered to stay in a room on the 13^th oor.

Answer:

(c) In 95% of samples of adult Americans, the proportion who would be bothered to stay in a room on the 13th oor is between 0.10 and 0.16.

Answer:

(d) We are 95% condent that 13% of adult Americans would be bothered to stay in a room on the 13th oor.

Answer:

Solution

(a) The statement is correct as 13% is the sample percentage out of 1006 respondents believing in the superstition and the margin of error is 3% with 95% confidence.

(b) The statement is false and the 95% confidence applies to the sample proportion and not not the level of confidence.

(c) This statement is correct.

(d) The statement is false since it is incorrect interpretation of confidence intervals.