Question

Listed below are the amounts of net worth​ (in millions of​ dollars) of the ten wealthiest celebrities in a country. Construct a 90​% confidence interval. What does the result tell us about the population of all​ celebrities? Do the data appear to be from a normally distributed population as​ required? 243 212 176 166 160 152 147 147 142 142

What is the confidence interval estimate of the population mean mu​? ​$ ? million < mu < ​$ ? million ​(Round to one decimal place as​ needed.)

What does the result tell us about the population of all​ celebrities? Select the correct choice below​ and, if​ necessary, fill in the answer​ box(es) to complete your choice.

A. Because the ten wealthiest celebrities are not a representative​ sample, this​ doesn't provide any information about the population of all celebrities.

B. We are confident that 90​% of all celebrities have a net worth between ​$ ? million and ​$ ?  million. ​(Round to one decimal place as​ needed.)

C. We are 90​% confident that the interval from ​$ ? million to ​$ ? million actually contains the true mean net worth of all celebrities. ​(Round to one decimal place as​ needed.)

Do the data appear to be from a normally distributed population as​ required?

A. ​No, but the points in the normal quantile plot lie reasonably close to a straight line and show some systematic pattern that is a straight line pattern.

B. ​Yes, but the points in the normal quantile plot do not lie reasonably close to a straight line or show a systematic pattern that is a straight line pattern.

C. ​No, because the points lie reasonable close to a straight​ line, but there is a systematic pattern that is not a straight line pattern.

D. ​Yes, because the pattern of the points in the normal quantile plot is reasonably close to a straight line.

Answer 1

Solution: Given that samples 243 212 176 166 160 152 147 147 142 142
sample n = 10, X = 168.7, sd = 33.6289, 90% Confidence interval
df = n-1 = 9, t = 1.833

90% Confidence interval for the mean = X +/- t*s/sqrt(n)
= 168.7 +/- 1.833*33.6289/sqrt(10)
= (149.2072, 188.1928)
= (149.2, 188.2)

=> We are 90​% confident that the interval from ​$ 149.2 million to​$ 188.2 million actually contains the true mean net worth of all celebrities.

=> No, because the points lie reasonable close to a straight​line, but there is a systematic pattern that is not a straight line pattern.