Exam 8: Confidence Interval Estimation

TABLE 8-10 The president of a university would like to estimate the proportion of the student population that owns a personal computer. In a sample of 500 students, 417 own a personal computer. -Referring to Table 8-10, a 95% confidence interval for the proportion of student population who own a personal computer is narrower than a 99% confidence interval.

TABLE 8-13 A university wanted to find out the percentage of students who felt comfortable reporting cheating by their fellow students. A surveyed of 2,800 students was conducted and the students were asked if they felt comfortable reporting cheating by their fellow students. The results were 1,344 answered "yes" and 1,456 answered "no." -Referring to Table 8-13, we are 99% confident that between 45.57% and 50.43% of the student population feel comfortable reporting cheating by their fellow students.

For a t distribution with 12 degrees of freedom, the area between - 2.6810 and 2.1788 is 0.980.

TABLE 8-15 A sales and marketing management magazine conducted a survey on salespeople cheating on their expense reports and other unethical conduct. In the survey on 200 managers, managers have caught salespeople cheating on an expense report 58% of the time, working a second job on company time 50% of the time, listing a "strip bar" as a restaurant on an expense report 22% of the time, and giving a kickback to a customer 19% of the time. -Referring to Table 8-15, we are 95% confident that between 51.16% and 64.84% of managers in the population have caught salespeople cheating on an expense report.

The t distribution allows the calculation of confidence intervals for means when the actual standard deviation is not known.

TABLE 8-9 A wealthy real estate investor wants to decide whether it is a good investment to build a high-end shopping complex in a suburban county in Chicago. His main concern is the total market value of the 3,605 houses in the suburban county. He commissioned a statistical consulting group to take a sample of 200 houses and obtained a sample average market price of $225,000 and a sample standard deviation of $38,700. The consulting group also found out that the average differences between market prices and appraised prices was $125,000 with a standard deviation of $3,400. Also the proportion of houses in the sample that are appraised for higher than the market prices is 0.24. -Referring to Table 8-9, what will be the 90% confidence interval for the population proportion of houses that will be appraised for higher than the market prices?

A major department store chain is interested in estimating the average amount its credit card customers spent on their first visit to the chain's new store in the mall. Fifteen credit card accounts were randomly sampled and analyzed with the following results: X = $50.50 and s2 = 400. Assuming the distribution of the amount spent on their first visit is approximately normal, what is the shape of the sampling distribution of the sample mean that will be used to create the desired confidence interval for µ?

TABLE 8-10 The president of a university would like to estimate the proportion of the student population that owns a personal computer. In a sample of 500 students, 417 own a personal computer. -Referring to Table 8-10, a 99% confidence interval will contain 99% of the student population who own a personal computer.

The head librarian at the Library of Congress has asked her assistant for an interval estimate of the mean number of books checked out each day. The assistant provides the following interval estimate: from 740 to 920 books per day. If the head librarian knows that the population standard deviation is 150 books checked out per day, and she asked her assistant for a 95% confidence interval, approximately how large a sample did her assistant use to determine the interval estimate?

The t distribution allows the calculation of confidence intervals for means for small samples when the population variance is not known, regardless of the shape of the distribution in the population.

TABLE 8-13 A university wanted to find out the percentage of students who felt comfortable reporting cheating by their fellow students. A surveyed of 2,800 students was conducted and the students were asked if they felt comfortable reporting cheating by their fellow students. The results were 1,344 answered "yes" and 1,456 answered "no." -Referring to Table 8-13, the critical value for a 99% confidence interval for this sample is_____ .

TABLE 8-8 A hotel chain wants to estimate the average number of rooms rented daily in each month. The population of rooms rented daily is assumed to be normally distributed for each month with a standard deviation of 24 rooms. -Referring to Table 8-8, during February, a sample of 25 days has a sample mean of 37 rooms. Use this information to calculate a 92% confidence interval for the population mean.

Holding the width of a confidence interval fixed, increasing the level of confidence can be achieved with a lower sample size.

The county clerk wants to estimate the proportion of retired voters who will need special election facilities. The clerk wants to find a 95% confidence interval for the population proportion which extends at most 0.07 to either side of the sample proportion. How large a sample must be taken to assure these conditions are met?

TABLE 8-10 The president of a university would like to estimate the proportion of the student population that owns a personal computer. In a sample of 500 students, 417 own a personal computer. -Referring to Table 8-10, it is possible that the 99% confidence interval calculated from the data will not contain the proportion of student population who own a personal computer.

The sample mean is a point estimate of the population mean.

TABLE 8-4 To become an actuary, it is necessary to pass a series of 10 exams, including the most important one, an exam in probability and statistics. An insurance company wants to estimate the mean score on this exam for actuarial students who have enrolled in a special study program. They take a sample of 8 actuarial students in this program and determine that their scores are: 2, 5, 8, 8, 7, 6, 5, and 7. This sample will be used to calculate a 90% confidence interval for the mean score for actuarial students in the special study program. -Referring to Table 8-4, the mean of the sample is____ , while the standard deviation of the sample is _____.

If you were constructing a 99% confidence interval of the population mean based on a sample of n=25 where the standard deviation of the sample s = 0.05, what will be the critical value of t?

It is desired to estimate the average total compensation of CEOs in the Service industry. Data were randomly collected from 18 CEOs and the 97% confidence interval was calculated to be ($2,181,260, $5,836,180). Based on the interval above, do you believe the average total compensation of CEOs in the Service industry is more than $3,000,000?

TABLE 8-11 The superintendent of a unified school district of a small town wants to make sure that no more than 5% of the students skip more than 10 days of school in a year. A random sample of 145 students from a population of 800 showed that 12 students skipped more than 10 days of school last year. -Referring to Table 8-11, what is the upper bound of the 95% one-sided confidence interval for the proportion of students who skipped more than 10 days of school last year?