For this problem, carry at least four digits after the decimal in your calculati

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 1006 supermarket shoppers revealed that 270 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. (Round your answer to four decimal places.)
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(b) Find a 95% confidence interval for p. (Round your answers to three decimal places.)

upper limit ?

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

upper limit ?

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

Explanation / Answer

b) To justify the point estimate both nP and n(1 - P) must be greater than 5.
nP = 1001(0.2727) since = P
= 273
n(1 - P) = 1001(1 - 0.2727)
= 728
since both nP and n(1 - P) are greater than 5 the point estimate is justified.


ii) margin of error

= ±z[ (1 - ) / n]
= ±1.96[0.2727(1 - 0.2727) / 1001]
= ±0.0276
= ±2.76%

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