Questions from statistical inference

Select the correct answer and write the appropriate letter in the space provided.
______ 1. A single number used to estimate a population parameter is
a. the confidence interval. b. the population parameter.
c. a point estimate. d. the mean of the population.

______ 2. A range of values constructed from sample data so that the parameter occurs within that range at a specified
probability is
a. a confidence interval. b. the population parameter.
c. a point estimate. d. the mean of the population

______ 3. The size of the standard error is affected by the standard deviation of the sample and
a. a confidence interval. b. the population parameter.
c. the point estimate. d. the sample size

______ 4. Suppose we select 100 samples from a population. For each sample we construct a 95 percent confidence interval. We could expect about 95 percent of these confidence intervals to contain
a. a sample mean. b. the population mean.
c. a point estimate. d. the standard deviation of the population

______ 5. The t distribution is a continuous distribution, with many similarities to
a. the confidence interval. b. the population parameter.
c. the standard normal distribution. d. the mean of the population

______ 6. The t distribution is used when the population is normal and
a. the population standard deviation is unknown.
b. the population standard deviation is known.
c. the point estimate is unknown.
d. the mean of the population is known.
______ 7. If the level of confidence is decreased from 95 percent to 90 percent, the width of the corresponding interval will
a. be increased. b. be decreased.
c. stay the same. d. not have an effect on the level of confidence

______ 8. The finite population correction factor is used when
a. the sample is more than 5 percent of the population.
b. the sample is less than 5 percent of the population.
c. the sample is larger than the population.
d. the population cannot be estimated.

______ 9. A 90 percent confidence interval for means indicates that 90 out of 100 similarly constructed intervals will include the
a. sample mean. b. sampling error.
c. z value d. population mean.

______ 10. The fraction, ratio, or percent indicating the part of the sample or the population having a particular trait of interest is
a. a confidence interval. b. the population parameter.
c. a point estimate. d. the proportion.

Part II Answer the following questions. Be sure to show essential work.

11. As part of a safety check, the Pennsylvania Highway Patrol randomly stopped 25 cars and checked their tire pressure. The sample mean was 32 pounds per square inch with a sample standard deviation of 2 pounds per square inch. Develop a 98 percent confidence interval for the population mean.

12. A human resource manager for Carver County is evaluating a recent effort to improve the health of the county's firefighters by providing an exercise room in each of the county's firehouses. Their records prior to installing the exercise rooms indicate that the mean weight of all county firefighters is 198 pounds with a standard deviation of 13 pounds. A random sample of 40 firefighters taken six months after the program was implemented revealed that the mean of the sample was 192 pounds. Construct a 96% confidence interval for the mean weight of all firefighters six months after the exercise rooms were installed. Assume that σ has not changed. Does it appear that the program is working?

13. Suppose that Carver County only has 250 firefighters. Construct a 96 percent confidence interval for the mean weight of all firefighters six months after the exercise rooms were installed.

14. A manufacturer of diamond drill bits for industrial production drilling and machining wishes to investigate the length of time a drill bit will last while drilling carbon steel. The production of the drill bits is very expensive, thus the number available for testing is small. A sample of 8 drill bits had a mean drilling time of 2.25 hours with a standard deviation of 0.5 hours. Is it reasonable for the manufacturer to claim that the drill bits will last 2.5 hours?

15. Of a random sample of 90 firms with employee stock ownership plans, 50 indicated that the primary reason for setting up the plan was tax related. Develop a 90 percent confidence interval for the population proportion of all such firms with this as the primary motivation.

16. A study of 305 computer chips found that 244 chips functioned properly. Develop a 99 percent confidence interval for the population proportion of properly functioning computer chips.

17. A correctional institution would like to report the mean amount of money spent per day on operating the facilities. How many days should be considered if a 95 percent confidence is used and the estimate is to be within one hundred dollars? The standard deviation is $400.

18. The Corporate Lawyer, a magazine for corporate lawyers, would like to report the mean amount earned by lawyers in their area of specialization. How large a sample is required if the 97 percent level of confidence is used and the estimate is to be within $2,500? The standard deviation is $16,000.

19. The Customer Relations Department at SkyBlue Airline wants to estimate the proportion of customers that do not check any luggage. The estimate is to be within 0.03 of the true proportion with 95 percent level of confidence. No estimate of the population proportion is available. How large a sample is required?

20. A survey is being conducted on a local mayoral election. If the poll is to have a 98 percent confidence level and must be within four percentage points, how many people should be surveyed?

Solution Summary

Step by step method for computing test statistic , confidence interval, and answers to multiple choice questions are given in the answer.