The personnel director of a large corporation wishes to study absenteeism among clerical workers at the corporation s central oce during the year.

The personnel director of a large corporation wishes to study absenteeism among clerical workers at the corporation s central office during the year. A random sample of 36 clerical workers reveals that the mean and the standard deviation of number of absences were 9.7 and 4.2 days, respectively.

(a) Construct a 95% confidence interval estimate of the mean number of absences for clerical workers during the year. (b) Interpret the confidence interval in part (a). (c) Suppose that the personnel director wishes to take the survey again. What sample size is needed to have 95% confidence in estimating the population mean to within 1.2 days? (d) Suppose that the personnel director also wishes to take a survey in a branch office. What sample size is needed to have 95% confidence in estimating the population mean to within 1 day if he knows that the number of absences there ranges from 0 to 22 days?

2. A simple random sample of 40 recorded speeds (in km/h) is obtained from cars traveling on a section of Al Ain - Abu Dhabi Highway. The sample has a mean of 124 km/h and a standard deviation of 10 km/h. Use a 0.05 significance level to test the claim that the mean speed of all cars is greater than the posted speed limit of 120 km/h.

3. A process that produces bottles of shampoo, when operating correctly, produces bottles whose contents weigh, on average, 20 ounces. A random sample of nine bottles from a single production run yielded the following content weights (in ounces):

21.4 19.7 19.7 20.6 20.8 20.1 19.7 20.3 20.9

Assuming that the population distribution is normal, test at the 5% level whether the process is operating correctly.

4. A courier service advertises that its average delivery time is less than 6 hours for local deliveries. A random sample of times for 12 deliveries to an address across town was recorded. These data are shown here.

3.03 6.33 6.50 5.22 3.56 6.76 7.98 4.82 7.96 4.54 5.09 6.46

(a) Is this sufficient evidence to support the courier’s advertisement, at the 5% level of significance? (b) What type of error could be made in this case? Describe it in words. (c) Check the assumptions of the procedure you use in part (a).