Question

Suppose a retailer claims that the average wait time for a customer on its support line is 185 seconds. A random sample of 57 customers had an average wait time of 175 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. 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.

B. 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.

Answer 1

Confidence Interval :-
X̅ ± Z( α /2) σ / √ ( n )
Z(α/2) = Z (0.05 /2) = 1.96
175 ± Z (0.05/2 ) * 47/√(57)
Lower Limit = 175 - Z(0.05/2) 47/√(57)
Lower Limit = 162.7984
Upper Limit = 175 + Z(0.05/2) 47/√(57)
Upper Limit = 187.2016
95% Confidence interval is ( 162.7984 , 187.2016 )

Since the value µ = 185  lies in the interval, hence we support the retailer's claim.

A. 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.