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Exam 8: Interval Estimation

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Question 31

Multiple Choice

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The sample size that guarantees all estimates of proportions will meet the margin of error requirements is computed using a planning value of p equal to

A) .01
B) .50
C) .51
D) .99

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Question 32

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If the standard deviation for the lifetimes of washing machines is estimated to be 800 hours, how large a sample must be taken in order to be 97% confident that the margin of error will not exceed 50 hours?

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Question 33

Multiple Choice

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It is known that the population variance equals 484. With a 0.95 probability, the sample size that needs to be taken to estimate the population mean if the desired margin of error is 5 or less is

The monthly starting salaries of students who receive an MBA degree have a standard deviation of $110. What size sample should be selected to obtain a 0.95 probability of estimating the mean monthly income within $20 or less?

A health club annually surveys its members. Last year, 33% of the members said they use the treadmill at least 4 times a week. How large of sample should be taken this year to estimate the percentage of members who use the treadmill at least 4 times a week? The estimate is desired to have a margin of error of 5% with a 95% level of confidence.

Computer Services, Inc. wants to determine a confidence interval for the average CPU time of their teleprocessing transactions. A sample of 196 transactions yielded a mean of 5 seconds. The population standard deviation is 1.4 seconds. Determine a 97% confidence interval for the average CPU time.

If we change a 95% confidence interval estimate to a 99% confidence interval estimate, we can expect the

A sample of 25 patients in a doctor's office showed that they had to wait an average of 35 minutes with a standard deviation of 10 minutes before they could see the doctor. Provide a 98% confidence interval estimate for the average waiting time of all the patients who visit this doctor. Assume the population of waiting times is normally distributed.

An interval estimate is used to estimate

The monthly incomes from a random sample of faculty at a university are shown below. Compute a 90% confidence interval for the mean of the population. The population of all faculty incomes is known to be normally distributed. Give your answer in dollars.

A reporter for a student newspaper is writing an article on the cost of off-campus housing. A sample was taken of 10 one-bedroom units within a half-mile of campus and the rents paid. The sample mean is $550 and the sample standard deviation is $60.05. Provide a 95% confidence interval estimate of the mean rent per month for the population of one-bedroom units within a half-mile of campus. We will assume this population to be normally distributed.

In order to determine the average weight of carry-on luggage by passengers in airplanes, a sample of 36 pieces of carry-on luggage was weighed. The average weight was 20 pounds. Assume that we know the standard deviation of the population to be 8 pounds. a.Determine a 97% confidence interval estimate for the mean weight of the carry-on luggage. b.Determine a 95% confidence interval estimate for the mean weight of the carry-on luggage.

A random sample of 81 children with working mothers showed that they were absent from school an average of 6 days per term. The population standard deviation is known to be 1.8 days. Provide a 90% confidence interval for the average number of days absent per term for all the children.

For the interval estimation of $\mu$ when $\sigma$ is assumed known, the proper distribution to use is the

A random sample of 36 magazine subscribers is taken to estimate the mean age of all subscribers. The data follow. Use Excel to construct a 90% confidence interval estimate of the mean age of all of this magazine's subscribers.

Exhibit 8-3 A random sample of 81 automobiles traveling on a section of an interstate showed an average speed of 60 mph. The distribution of speeds of all cars on this section of highway is normally distributed, with a standard deviation of 13.5 mph. -Refer to Exhibit 8-3. The value to use for the standard error of the mean is

You are given the following information obtained from a random sample of 4 observations taken from a large, normally distributed population. Construct a 95% confidence interval for the mean of the population.

Political Science, Inc. (PSI) specializes in voter polls and surveys designed to keep political office seekers informed of their position in a race. Using telephone surveys, interviewers ask registered voters who they would vote for if the election were held that day.In a recent election campaign, PSI found that 220 registered voters, out of 500 contacted, favored a particular candidate. a. PSI wants to develop a 95% confidence interval estimate for the proportion of the population of registered voters that favors the candidate. b. Suppose that PSI would like 99% confidence that the sample proportion is within +/- .03 of the population proportion. How large a sample size is needed to provide the desired margin of error?

In determining an interval estimate of a population mean when $\sigma$ is unknown, we use a t distribution with

In order to determine how many hours per week freshmen college students watch television, a random sample of 256 students was selected. It was determined that the students in the sample spent an average of 14 hours. The standard deviation is 3.2 hours per week for all freshman college students. a.Provide a 95% confidence interval estimate for the average number of hours that all college freshmen spend watching TV per week. b.Suppose the sample mean came from a sample of 25 students. Provide a 95% confidence interval estimate for the average number of hours that all college freshmen spend watching TV per week. Assume that the hours are normally distributed.