Question

Sleeping outlier: A simple random sample of eight college freshmen were asked how many hours of sleep they typically got per night. The results were 24 6 8.5 8 8.5 7.5 6.5 9 Send data to Excel Notice that one joker said that he sleeps 24 a day. Part: 0/ 3 Part 1 of 3 (a) The data contain an outlier that is clearly a mistake. Eliminate the outlier, then construct a 90 % confidence interval for the mean amount of sleep from the remaining values. Round the answers to at least two decimal places. A 90% confidence interval for the mean amount of sleep from the remaining values is <H<

Answer 1

From the given data we remove outlier value 24 and find the sample mean and sample standard deviation for remaining data.

For n = 7 , Xbar = 7.714 and s = 1.113

The 90% confidence interval for the mean amount of sleep from the remaining values

xbar - t_{​​​​​​a/2, n -1}*(s/√n) < $\mu$ < Xbar + t_{​​​​​​a/2,n-1}*(s/√n)

For a = 0.10 , d.f = n -1 = 6

t_{​​​​​​0.05,6 = 1.943}

_{7.714 - 1.943 *(1.113/√7) < $\mu$ < 7.714 + 1.943*(1.113/√7)}

_{6.897 <  $\mu$ < 8.531}