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.

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