2. A simple random sample of 50 calls is monitored at an in-bound call center and

the average length of the calls is 6 minutes. The population standard deviation

is unknown. Instead the sample standard deviation s is also calculated from the

sample and is found to be 4 minutes.

a. Construct a 99% confidence interval (using the t-distribution) for the

average length of inbound calls.

b. What is the margin of error at the 95% confidence level?

c. Do we need to make any assumption on the distribution of the length of

inbound calls at this call center? Why or why not?

3. According to a previous study, check out times at a supermarket are between 2

to 7 minutes (120 to 8400 seconds.) A survey involving a random sample of

customers of the supermarket is planned and the first order of

business is to decide on an appropriate sample size. The 95% level of

confidence will be used.

a. What is the planning value for the population standard deviation to be

used in the sample size formula for estimating the population mean

checkout time?

b. How large should the sample size be if the desired margin of error is 30

seconds?