Question

A magazine provided results from a poll of 1500 adults who were asked to identify their favorite pie. Among the 1500 respondents, 14​% chose chocolate​ pie, and the margin of error was given as ±33 percentage points. Describe what is meant by the statement that​ "the margin of error was given as ±33 percentage​ points."

A. The statement indicates that the study is 100%-3%=97% confident that the true population percentage of people that prefer chocolate pie is 14%.

B. The statement indicates that the study is only 3% confident that the true population percentage of people that prefer chocolate pie is exactly 14%.

C.The statement indicates that the true population percentage of people that prefer chocolate pie is in the interval 14%±3%.

D.The statement indicates that the interval 14%±3% is likely to contain the true population percentage of people that prefer chocolate pie.

Answer 1

D.The statement indicates that the interval 14%±3% is likely to contain the true population percentage of people that prefer chocolate pie

Explanation:

Lower and upper limit of the comfidence interval is calculated based on the margin of error. The point estimate (sample mean) minus margin of error is the result of lower limit. and The point estimate (sample mean) plus margin of error is the result of upper limit.

so here the 14 % is the point estimate with plue or minus are considered as the intervals.

For example: (Refer column F for calcualtion procedure)