Exam 9: Estimation From Sample Data

In surveying a simple random sample of 1000 assistant professors,we found that 573 of them felt they were underpaid by at least $3500.Based on these results,we have a 95% confidence that the proportion of the population of assistant professors who share this sentiment is between .548 and .598. Identify the: Confidence level: Confidence coefficient:

Explain how precision for a confidence interval is related to the width of the confidence interval.

The sample statistic s is an unbiased estimator of the population parameter $\text { ? }$ when (n - 1)is used as a divisor when we calculate the standard deviation of the sample.

Which of the following statements are correct?

Coffee for breakfast in the 1960's was a commonplace method of becoming more alert for classes among college students.However,coffee makers have seen a decline in U.S.coffee consumption and are obviously concerned about it.One coffee maker decides to estimate the proportion of college students (likely candidates for coffee)who drink coffee for breakfast nationally.The proportion of the total population who drink coffee for breakfast is about 0.55.The coffee maker decides to use 0.55 as the value for p in determining the sample size to select from among college students.A 92% confidence interval is chosen and the estimate,p,is to be within 0.05 of the true proportion of college students who drink coffee for breakfast.Compute the needed sample size.

An estimator is unbiased if the expected value of the ____________________ is the same as the actual value of the ____________________ it is intended to estimate.

A cost accountant wished to establish the average amount, $\mu$ ,spent by executives per day on travel and lodging.Then a comparison,between the average and the amount turned in to be reimbursed,will be made and unreasonably high or low expense amounts audited.A random sample of 50 executive expense receipts is taken.The average in the sample was $208.From a similar survey the standard deviation of the amounts is approximately $\text { σ }$ = $29.The accountant prepares a 90-percent confidence level for $\mu$ .What is its maximum error?

How can one reduce the width of a confidence interval for a given level of confidence?

A fund raiser for United Way wants to know the average annual income of workers in a very large vegetable processing plant.She is able to obtain a sample of 30 annual wage levels (in thousands).She finds that the summation of the wages for the 30 is 370.7 and the standard deviation of 3.3.What estimate may be used for $\mu$ ?

A cost accountant wishes to establish the average amount, $\mu$ ,spent by executives per day on travel and lodging.The population standard deviation $\text { σ}$ = $29.The accountant wants to be 90-percent confident that the estimate, $\bar { x }$ ,obtained is within $7 of the true mean.How large a sample is needed?

In using the standard normal distribution to construct a confidence interval for the population mean,what assumptions are necessary if the sample size n is less than 30?

From a community of 80 homes,the EPA took a random sample and found the presence of lead in the tap water.In the 10 homes sampled,the average lead content was 12 parts per billion with s = 5 pts/billion.Construct a 99% confidence interval estimate for the population mean. ____________________ to ____________________ Do you feel that the homes exceed the EPA recommended maximum of 15 pts/billion? Explain your answer.

A large bank in a metropolitan area has a large number of secured loans on apartment facilities throughout the area.Local economic indicators suggest the percentage of vacant apartments ranges from 7% to 10%.Concerned about the borrowers' ability to meet loan obligations on time the bank decides to sample from the apartments used to secure loans.The officer responsible for the sample decides to allow a maximum error of the estimate of 0.01 with 99 percent confidence.The officer wishes to take a sample large enough to cover all proportions within the estimated vacancy range.Compute the sample size needed for this study.

Determine the limits of the 85% confidence interval for $\pi$ ,given that n = 50; and p = 0.20. ____________________ to ____________________

In an effort to determine the average loaded weight of trucks leaving a gypsum wallboard plant,a random sample is to be taken from the 600 trucks scheduled for this month.From past studies,the population standard deviation is known to be 2500 lbs.A 95-percent confidence interval is to be used and the average, $\mu$ ,is to be estimated within 500 pounds.Determine the sample size needed.

A marketing class is engaged in a project to estimate the proportion of homes receiving both HBO and ShowTime cable service.The class plans to use a confidence coefficient of 0.95 and a maximum error of the estimate equal to 0.10.If 2500 homes in this city receive cable service,determine the sample size for the class to use.

Raising in-state and out-of-state tuition is supposed to reduce the number of students in state supported universities.The registrar of a university wants to estimate the proportion, $\pi$ ,of students who are paying out-of-state tuition on the installment plan (to later be compared with in-state installment plan payers).A random sample of 80 students who live out-of-state is taken and 50 of them pay tuition on the installment plan.Find a 99-percent confidence interval for $\pi$ based on these data. ____________________ to ____________________

If a sample has 16 observations from a normal population and a 90% confidence estimate for $\mu$ is needed,the appropriate t-score is 2.12.

An auditor for a large oil corporation has taken a random sample of monthly credit card charges for 32 individual (non-corporate)accounts.She found a mean of $81.76.Assume that the population standard deviation is 48.2.A 98% confidence interval estimate for the population mean of individual credit card charges would be:

Suppose that the amount of time teenagers spend on the internet is normally distributed with a standard deviation of 1.5 hours.A sample of 100 teenagers is selected at random,and the sample mean computed as 6.5 hours. A)Determine the 95% confidence interval estimate of the population mean. ____________________ to ____________________ B)Interpret what the interval estimate in part (a)tells you.