Question

Suppose a retailer claims that the average wait time for a customer on its support line is 190 seconds. A random sample of 41 customers had an average wait time of 179 seconds. Assume the population standard deviation for wait time is 47 seconds. Using a 95​% confidence​ interval, does this sample support the​ retailer's claim?

Using a 95​% confidence​ interval, does this sample support the​ retailer's claim? Select the correct choice​ below, and fill in the answer boxes to complete your choice.

​(Round to two decimal places as​ needed.)

A. No​,because the​ retailer's claim is not between the lower limit of __ seconds and the upper limit of __ seconds for the mean wait time.

B. Yes​, because the​ retailer's claim is nothing between the lower limit of __ seconds and the upper limit of ___ seconds for the mean wait time.

Answer 1

95% confidence interval for is

- Z * / sqrt(n) < < + Z * / sqrt(n)

179 - 1.96 * 47 / sqrt(41) < < 179 + 1.96 * 47 / sqrt(41)

164.61 < < 193.39

95% CI is (164.61 , 193.39)

Yes​, because the​ retailer's claim is between the lower limit of 164.61 seconds and the upper limit of

193.39 seconds for the mean wait time.