largefamily-held department store had the business objective of improving its response to complaints. The variable of interest was defined as the number of days between when the complaint was made and when it was resolved. Data were collected from 40 complaints that were made in the last year. Use the data to complete parts(a) through(d) below.

numbers: 34 13 5 26 37 117 14 33 22 2 168 19 8 83 63 27 48 158 34 150 7 10 26 12 67 20 30 53 15 25 22 30 5 24 20 14 29 63 12 43

Part a) Construct a 95% confidence interval estimate for the population mean number of days between the receipt of a complaint and the resolution of the complaint.

the 95% confidence interval estimate is from _____ days to ___ days (round to one decimal place)

Part b)

What assumption must you make about the population distribution in order to construct the confidence interval estimate in(a)?

A.

The number of complaints per day follows the t distribution.

B.

The number of days to resolve complaints is normally distributed.

C.

The number of complaints per day is normally distributed.

D.

The number of days to resolve complaints follows the t distribution.

part c)

Do you think that the assumption needed in order to construct the confidence interval estimate in(a) isvalid? Explain.

A.

No, the data suggest the population distribution is skewed to the right.

B.

Yes, the data suggest the population distribution is approximately normal.

C.

No, the data suggest the population distribution is skewed to the left.

D.

Yes, the data suggest the population distribution approximately follows the t distribution.

part d)

What effect might your conclusion in(c) have on the validity of the results in(a)?

A.

Since the data suggest the population distribution isskewed, use of the t distribution is notappropriate, so the results are not valid.

B.

Since the sample size is fairlylarge, the t distribution can still be used due to the Central LimitTheorem, so the results are valid.

C.

Since the data suggest the population distribution is approximatelynormal, use of the t distribution isappropriate, so the results are valid.

D.

Since the data suggest the population distribution follows the tdistribution, use of the t distribution isappropriate, so the results are valid.