Exam 8: Confidence Interval Estimation

The confidence interval obtained will always correctly estimate the population parameter.

TABLE 8-15 A sales and marketingmanagement magazine conducted a surveyonsalespeople cheatingon their expense reports and other unethicalconduct. In thesurvey on 200 managers, managers have caughtsalespeople cheatingonanexpense report $58 \%$ of the time, workinga second job oncompany time $50 \%$ of the time, listinga "strip bar" as a restauranton anexpense report $22 \%$ of the time, and givinga kickback to a customer $19 \%$ of the time. -Referring to Table 8-15, the critical value for a 95% confidence interval estimate of the population proportion of managers who have caught salespeople cheating on an expense report is______ .

The head of a computer science department is interested in estimating the proportion of students entering the department who will choose the new computer engineering option. A preliminary sample indicates that the proportion will be around 0.25. Therefore, what size sample should the department head take if she wants to be 95% confident that the estimate is within 0.10 of the true proportion?

TABLE 8-7 After an extensive advertising campaign, the manager of a company wants to estimate the proportion of potential customers that recognize a new product. She samples 120 potential consumers and finds that 54 recognize this product. She uses this sample information to obtain a 95% confidence interval that goes from 0.36 to 0.54. -Referring to Table 8-7, it is possible that the true proportion of people that recognize the product is between 0.36 and 0.54.

The width of a confidence interval equals twice the sampling error.

TABLE 8-5 The actual voltages of power packs labeled as 12 volts are as follows: 11.77, 11.90, 11.64, 11.84, 12.13, 11.99, and 11.77. -Referring to Table 8-5, the critical value for a 99% confidence interval for this sample is______

A 99% confidence interval estimate can be interpreted to mean that

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, a 99% confidence interval for the proportion of student population who feel comfortable reporting cheating by their fellow students is from____ to____

A university dean is interested in determining the proportion of students who receive some sort of financial aid. Rather than examine the records for all students, the dean randomly selects 200 students and finds that 118 of them are receiving financial aid. If the dean wanted to estimate the proportion of all students receiving financial aid to within 3% with 99% reliability, how many students would need to be sampled?

Other things being equal, the confidence interval for the mean will be wider for 95% confidence than for 90% confidence.

An economist is interested in studying the incomes of consumers in a particular region. The population standard deviation is known to be $1,000. A random sample of 50 individuals resulted in an average income of $15,000. What is the width of the 90% confidence interval?

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, if he wants a 95% confidence on estimating the true population average market price of the houses in the suburban county to be within $10,000, how large a sample will he need?

A prison official wants to estimate the proportion of cases of recidivism. Examining the records of 250 convicts, the official determines that there are 65 cases of recidivism. A 99% confidence interval for the proportion of cases of recidivism would go from_________ to_______ .

TABLE 8-6 A sample of salary offers (in thousands of dollars) given to management majors is: 28, 31, 26, 32, 27, 28, 27, 30, 31, and 29. Using this data to obtain a 95% confidence interval resulted in an interval from 27.5 to 30.3. -Referring to Table 8-6, 95% of all confidence intervals constructed similarly to this one with a sample size of 10 will contain the mean of the population.

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 90% confidence interval calculated from the same data would be narrower than a 99% confidence interval.

The t distribution is used to construct confidence intervals for the population mean when the population standard deviation is unknown.

TABLE 8-5 The actual voltages of power packs labeled as 12 volts are as follows: 11.77, 11.90, 11.64, 11.84, 12.13, 11.99, and 11.77. -Referring to Table 8-5, it is possible that the 99% confidence interval calculated from the data will not contain the mean voltage for the sample.

Suppose a 95% confidence interval for µ turns out to be (1,000, 2,100). Give a definition of what it means to be "95% confident" as an inference.

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 critical value used in constructing a 90% confidence interval is____

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, the parameter of interest is the average number of students in the population who own a personal computer.