For this problem, carry at least four digits after the decimal in your calculations. Answers may vary slightly due to rounding.

In a marketing survey, a random sample of728women shoppers revealed that622remained loyal to their favorite supermarket during the past year (i.e., did not switch stores).

(a) Letprepresent the proportion of all women shoppers who remain loyal to their favorite supermarket. Find a point estimate forp. (Round your answer to four decimal places.)

(b) Find a 95% confidence interval forp. (Round your answers to three decimal places.)

lower limit?

upper limit?

Give a brief explanation of the meaning of the interval.

We are 95% confident that the true proportion of loyal women shoppers falls within this interval.

We are 5% confident that the true proportion of loyal women shoppers falls above this interval.

We are 5% confident that the true proportion of loyal women shoppers falls within this interval.

We are 95% confident that the true proportion of loyal women shoppers falls outside this interval.

(c) As a news writer, how would you report the survey results regarding the percentage of women supermarket shoppers who remained loyal to their favorite supermarket during the past year?

Report the margin of error.

Reportpalong with the margin of error.

Report the confidence interval.

Reportp.

What is the margin of error based on a 95% confidence interval? (Round your answer to three decimal places.)