Which of the parameters, the mean or median, do you think best represents the

months, a random sample of the records of 38 customers who had complaints revealed a mean time of 28.7 minutes with a standard deviation of 3.8 minutes. a. Give a point estimate of the mean time required to handle a customer complaint. b. What is the standard deviation of the point estimate given in a?

c. Construct a 95 confidence on the mean time to handle a complaint after imple-

menting the plan. Interpret the confidence interval for the office manager.

d. Is there sufficient evidence that the incentive plan has reduced the mean time to handle

a complaint? Env. 5.64 The concentration of mercury in a lake has been monitored for a number of years. Mea- surements taken on a weekly basis yielded an average of 1.20 mgm 3 milligrams per cubic meter with a standard deviation of .32 mgm 3 . Following an accident at a smelter on the shore of the lake, 15 measurements produced the following mercury concentrations. 1.60 1.77 1.61 1.08 1.07 1.79 1.34 1.07 1.45 1.59 1.43 2.07 1.16 0.85 2.11 a. Give a point estimate of the mean mercury concentration after the accident. b. Construct a 95 confidence interval on the mean mercury concentration after the accident. Interpret this interval.

c. Is there sufficient evidence that the mean mercury concentration has increased since

the accident? Use a ⫽ .05.

d. Assuming that the standard deviation of the mercury concentration is .32 mgm

3 , calculate the power of the test to detect mercury concentrations of 1.28, 1.32, 1.36, and 1.40. Med. 5.65 Over the years, projected due dates for expectant mothers have been notoriously bad at a large metropolitan hospital. The physicians attended an in-service program to develop tech- niques to improve their projections. In a recent survey of 100 randomly selected mothers who had delivered a baby at the hospital since the in-service, the average number of days to birth beyond the projected due date was 9.2 days with a standard deviation of 12.4 days. a. Describe how to select the random sample of 100 mothers. b. Estimate the mean number of days to birth beyond the due date using a 95 confidence interval. Interpret this interval.

c. If the mean number of days to birth beyond the due date was 13 days prior to the in-

service, is there substantial evidence that the mean has been reduced? What is the level of significance of the test?

d. What factors may be important in explaining why the doctors’ projected due dates

are not closer to the actual delivery dates? Med. 5.66 In a standard dissolution test for tablets of a particular drug product, the manufacturer must obtain the dissolution rate for a batch of tablets prior to release of the batch. Suppose that the dissolution test consists of assays for 24 randomly selected individual 25 mg tablets. For each test, the tablet is suspended in an acid bath and then assayed after 30 minutes. The results of the 24 assays are given here. 19.5 19.7 19.7 20.4 19.2 19.5 19.6 20.8 19.9 19.2 20.1 19.8 20.4 19.8 19.6 19.5 19.3 19.7 19.5 20.6 20.4 19.9 20.0 19.8

a. Using a graphical display, determine whether the data appear to be a random sample

from a normal distribution.

b. Estimate the mean dissolution rate for the batch of tablets, for both a point estimate

and a 99 confidence interval.

c. Is there significant evidence that the batch of pills has a mean dissolution rate less

than 20 mg 80 of the labeled amount in the tablets? Use a ⫽ .01.

d. Calculate the probability of a Type II error if the true dissolution rate is 19.6 mg. Bus.

5.67 Statistics has become a valuable tool for auditors, especially where large inventories are in- volved. It would be costly and time consuming for an auditor to inventory each item in a large op- eration. Thus, the auditor frequently resorts to obtaining a random sample of items and using the sample results to check the validity of a company’s financial statement. For example, a hospital