You are opening your own wedding planning business and are conducting some marke

Question

You are opening your own wedding planning business and are conducting some market research. According to The Knot Real Weddings Study, the average cost of a wedding in the U.S. is $35,000.

You are skeptical about whether these numbers apply to the Piedmont Triad area—your target market—and so you decide to conduct your own survey. After randomly sampling 40 recently married couples, you find an average cost of $32,000 with a standard deviation of $10,000.

When you conduct your survey, you also ask whether the couple had a destination wedding. Seven out of the 40 couples reported having a destination wedding.

A. Find the 80% confidence interval for the proportion of couples that have a destination wedding. Find the standard error of the proportion.

B. Find the critical value.

C. Put it together to find the confidence interval.

D. You find out that respondents to The Knot’s survey were recruited from members of TheKnot.com. Do you trust that the survey results come from a representative sample? Why or why not?

Explanation / Answer

Sample mean of average cost of a destination wedding x = $ 32,000

Sample standard deviation of average cost of a destination wedding s = $10,000

(A)  80% confidence interval for the proportion of couples that have a destination wedding

Here Sample proportion p^ = 7/40 = 0.175

80% confidence interval for the proportion of couples that have a destination wedding = P^ +- Z80% sqrt[p^ * (1-p^)/N]

Standard error of the proportion = sqrt[p^ * (1-p^)/N] = sqrt [0.175 * 0.825/40] = 0.06

critical test statistic for 80% confidence interval = 1.28

= 0.175 +- 1.28 * sqrt[0.175 * 0.825/ 40]

= 0.175 +- 1.28 * 0.06

= (0.098, 0.252)

(D) No, the survey results doesn't come from a representative sample as data comes from a signle website that doesn't show randomness as only internet users can avail this website. SO, that eliminates possibility of random nature of sample.

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