6. A simple random sample of 20 recent U.S. wedding yielded the following data o

Question

6. A simple random sample of 20 recent U.S. wedding yielded the following data on wedding costs, in dollars. Assume that recent wedding costs in the U.S are normally distributed with a standard deviation of $8100. 19496 27806 30098 32269 23789 21203 13360 40406 29288 33178 35050 14554 34081 42646 21083 18460 27896 24053 19510 a. Use the data to obtain a point estimate for the population mean wedding cost, u, of all recent U.S. weddings. (Note: The sum of the data is $526,538) b. Is your point estimate in part (a) likely to equal u exactly? Explain your answer. c. Determine a 95% confidence interval for the mean cost., of all recent U.S weddings. d. Interpret your result in part (c).

Explanation / Answer

a) sample mean = 526538/20 = 26326.9

sample mean is point estimate for the population mean

b)

No, sample mean is an unbiased estimator of population mean

but sample mean is not likely to equal mu exactly

c) 95 % confidence interval

(26326.9 - 1.96 * 8100/sqrt(20) , 26326.9 + 1.96 * 8100/sqrt(20))

=(22776.9185 , 29876.8815)

d)

we are 95% confident that the population mean lies in this confidence interval

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