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

-- What is the point estimate of the proportion of destination weddings for the Piedmont Triad?

-- Find the standard error of the proportion.

-- Find the critical value.

-- Put it together to find the confidence interval.

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?

Answer 1

given that

sample size =n=40

number of couples wants destination wedding =x=7

1)

point estimate of proportion of destination wedding is given by

2)

the standard error is given by

3)

since confidence level is 80% hence critical value is given by

from Z table

P(Z>1.28)=0.1

So

critical Value =Z0.1=1.28

4)

now 80% confidence interval is given by

so interval is (0.098,0.252)

yeah we will trust the survey results as these values are observed from couples so we can trust the survey.