Question

Suppose a retailer claims that the average wait time for a customer on its support line is 173 seconds. A random sample of 56 customers had an average wait time of 164 seconds. Assume the population standard deviation for wait time is 50 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 nothing seconds and the upper limit of nothing seconds for the mean wait time.

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

Answer 1

Solution:

Given:

Claim: the average wait time for a customer on its support line is 173 seconds.

Sample size = n = 56

Sample mean = seconds.

The population standard deviation = seconds

We have to find 95​% confidence​ interval for  the average wait time for a customer on its support line.

Formula:

where

We need to find zc value for c=95% confidence level.

Find Area = ( 1 + c ) / 2 = ( 1 + 0.95) /2 = 1.95 / 2 = 0.9750

Look in z table for Area = 0.9750 or its closest area and find z value.

Area = 0.9750 corresponds to 1.9 and 0.06 , thus z critical value = 1.96

That is : Zc = 1.96

Thus

thus

Using a 95​% confidence​ interval, does this sample support the​ retailer's claim?

B. Yes​, because the​ retailer's claim is 173 between the lower limit of 150.90 seconds and the upper limit of 177.10 seconds for the mean wait time.