Question

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 of 988 supermarket shoppers revealed that 266 always stock up on an item when they find that item at a real bargain price.

(a) Let p represent the proportion of all supermarket shoppers who always stock up on an item when they find a real bargain. Find a point estimate for p. (Enter a number. Round your answer to four decimal places.)

(b) Find a 95% confidence interval for p. (For each answer, enter a number. 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 shoppers who stock up on bargains falls outside this interval.

We are 95% confident that the true proportion of shoppers who stock up on bargains falls within this interval.    

We are 5% confident that the true proportion of shoppers who stock up on bargains falls within this interval.

We are 5% confident that the true proportion of shoppers who stock up on bargains falls above this interval.

(c) As a news writer, how would you report the survey results on the percentage of supermarket shoppers who stock up on items when they find the item is a real bargain?

Report the margin of error.

Report p̂ along with the margin of error.    

Report p̂.

Report the confidence interval.

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

What is the minimal sample size needed for a 95% confidence interval to have a maximal margin of error of 0.1 in the following scenarios? (For each answer, enter a number. Round your answers up the nearest whole number.)

(a) a preliminary estimate for p is 0.16

(b) there is no preliminary estimate for p

Answer 1