# Confidence interval for mean

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8.2 (1) If `X = 125, s = 8, and n = 64, construct a 95% confidence interval estimate of the population mean, m.

8.8 (2) The quality control manager at a light bulb factory needs to estimate the mean life of a large shipment of light bulbs. The standard deviation is 100 hours. A random sample of 64 bulbs indicated a sample mean life of 350 hours.

Construct a 95% confidence interval estimate of the population mean life of light bulbs in this shipment.

B.Do you think that the manufacturer has the right to state that the light bulbs last an average of 400 hours? Explain.

C. Suppose the standard deviation changes to 80 hours. What are your answers for A and B?

8.10 (3) Determine the critical value of t in each of the following circumstances:

1 - a = 0.95, n = 10

1 - a = 0.99, n = 10

1 - a = 0.95, n = 32

1 - a = 0.95, n = 65

1 - a = o.90, n = 16

8.12 (4) If `X = 50, S = 15, and n = 16, and assuming that the population is normally distributed, construct a 99% confidence interval estimate of the population mean, m.

8.14 (5) Construct a 95% confidence interval for the population mean, based on the numbers 1, 2, 3, 4, 5, 6, and 20. Change the number 20 to 7 and recalculated the confidence interval. Using these results, describe the effect of the outlier the extreme value) on the confidence interval.

8.16 (6) Southside Hospital is doing a turnaround study on those who go for a stress test. Turnaround time is defined as the time from when the test is ordered to when the radiologists signs off on the test results. Initially, the mean turnaround time for a stress test was 68 hours. After initiating changes in the process, they took a sample of 50 patients to see if there was improvement. In this sample, the mean turnaround time was 32 hours, with a standard deviation of 9 hours.

Construct a 95% confidence interval for the population mean turnaround time.

Interpret the interval constructed in (A).

8.20 (7) A large family-based department store selling furniture and flooring, including carpet, has undergone a major expansion in the past several years. In particular, the flooring dept. had expanded from 2 installation crews to an installation supervisor, a measurer, and 15 installation crews. Last year, there were 50 complaints concerning carpet installation. The following data, in the file, represents the number of days between the receipt of a complaint and the resolution of the complaint: (continued on next page)

54 3 35 137 31 27 152 1 123 81 74 27

11 19 126 110 110 29 61 35 94 31 26 5

12 4 165 32 29 28 28 26 25 1 14 14

13 10 5 17 4 52 30 22 36 26 20 23 33 68

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

8.25 (9) If n = 400 and X = 25, construct a 99% confidence interval estimate of the population proportion.

8.27 (10) According to the Center of Work - Life Policy, a survey of 500 highly educated women who left careers for family reasons found that 66% wanted to return to work.

Construct a 95% confidence interval for the population proportion of highly educated women who left careers for family reasons who want to return to work. Then, interpret the interval in A.

8.29 (11) A telephone survey of 1900 older consumers found that 27% said they didn't have enough time to be good money managers.

Construct a 95% confidence interval for the population proportion of older consumers

Who think they don't have enough time to be good money managers. Then, interpret the interval in A.

8.43 (12) An advertising agency that serves a major radio station wants to estimate the mean amount f time that the station's audience spends listening to the radio daily. From past studies, the standard deviation is estimated at 45 minutes/day.

What sample size is needed if the agency wants to be 90% confident of being correct to within +- 5 minutes?

If 99% confidence is desired, what sample size is necessary?

8.46 (13) In 2005, 34% of workers reported that their jobs were more difficult, with more stress, and 37& reported that they worry about retiring comfortably. Consider a follow-up study to be conducted in the near future.

What sample size is needed to estimate the population proportion of workers who reported that their jobs were more difficult, with more stress, to within +- 0.02 with 90% confidence?

What sample size is needed to estimate the population proportion of workers who worry about retiring comfortably to within +- 0.02 with 95% confidence?

8.50 (14) A sample of 25 is selected from a population of 500 items. The sample mean is 25.7, and the sample standard deviation is 7.8. Construct a 99% confidence interval estimate of the population total.

8.54 (15) The personnel department of a large corporation employing 3,000 workers wants to estimate the family dental expenses of its employees to determine the feasibility of providing a dental insurance plan. A random sample of 10 employees reveals the following family dental expenses (in dollars) for the preceding year:

$110 362 246 85 510 208 173 425 316 179

Construct a 90% confidence interval estimate of the total family dental expense for all employees in the preceding year.

8.56 (16) A sample of 150 items selected from a population of 4,000 invoices at the end of a period of time revealed that in 13 cases, the customer failed to take the discount to which he or she was entitled. The amounts (in dollars) of the 13 discounts that were not taken were as follows: $6.45 15.32 97.36 230.63 104.18 84.92 132.76 66.12 26.55 129.43 88.32 47.81 89.01

Construct a 99% confidence interval estimate of the population total amount of discounts NOT taken.

8.58 (17) An internal control policy for a company is that a check can be issued only after the accounts payable manager initials the invoice. The tolerable exception rate for this internal control is 0.04. During an audit, a sample of 300 invoices is examined from a population of 10,000 invoices, and 11 invoices are found to violate the internal control.

Calculate the upper bound for a 95% one-sided confidence interval estimate for the rate of non-compliance of the internal control.

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This solution gives the step by step method for computing confidence interval for mean.