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.

1. Find the 90% confidence interval for the mean wedding cost in the Piedmont Triad.

a. What is the point estimate of the mean wedding cost for the Piedmont Triad?

b. Find the standard error of the mean.

c. Find the critical value. (You’ll need to decide whether to use a z-score or a t-score.)

d. Put it together to find the confidence interval.

2. What is the margin of error for the 90% confidence interval?

3. Interpret the 90% confidence interval for the mean wedding cost in the Piedmont Triad. Does the interval include the average for the U.S.? Would you conclude that the cost of weddings in the Piedmont Triad is different from the rest of the U.S.?

4. Find the 95% confidence interval for the mean wedding cost for the Piedmont Triad. How does it compare to the 90% confidence interval (narrower or wider)? Does your conclusion about the Piedmont Triad being different change?

5. Suppose you wanted to keep the confidence level at 90%, but you wanted to decrease the width of the interval. How could you do this?

6. 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.

a. What is the point estimate of the proportion of destination weddings for the Piedmont Triad

b. Find the standard error of the proportion.

c Find the critical value.

d. Put it together to find the confidence interval.

7. 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