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 996 supermarket shoppers revealed that 272 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.)

(b) Find a 95% confidence interval for p. (round your answers to three decimal places.)

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

Explanation / Answer

a.
stock up on an item(x)=272
Sample Size(n)=996
Sample proportion = x/n =0.273

b.
Margin of Error = Z a/2 Sqrt(p*(1-p)/n))
x = Mean
n = Sample Size
a = 1 - (Confidence Level/100)
Za/2 = Z-table value
CI = Confidence Interval
Mean(x)=272
Sample Size(n)=996
Sample proportion =0.273
Margin of Error = Z a/2 * ( Sqrt ( (0.273*0.727) /996) )
= 1.96* Sqrt(0)
=0.028

c.
Confidence Interval For Proportion
CI = p ± Z a/2 Sqrt(p*(1-p)/n)))
x = Mean
n = Sample Size
a = 1 - (Confidence Level/100)
Za/2 = Z-table value
CI = Confidence Interval

Confidence Interval = [ 0.273 ±Z a/2 ( Sqrt ( 0.273*0.727) /996)]
= [ 0.273 - 1.96* Sqrt(0) , 0.273 + 1.96* Sqrt(0) ]
= [ 0.245,0.301]

Related Questions

Navigate

• Browse (All)
• Browse F
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.