Exam 8: Confidence Interval Estimation

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 the total numbers of student population who feel comfortable reporting cheating by their fellow students is between 0.4557 and 0.5043.

The t distribution approaches the standardized normal distribution when the number of degrees of freedom increases.

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 the salary offers are between 27.5 and 30.3.

As an aid to the establishment of personnel requirements, the director of a hospital wishes to estimate the mean number of people who are admitted to the emergency room during a 24-hour period. The director randomly selects 64 different 24-hour periods and determines the number of admissions for each. For this sample, $\overline{X}$ = 19.8 and s² = 25. Using the sample standard deviation as an estimate for the population standard deviation, what size sample should the director choose if she wishes to estimate the mean number of admissions per 24-hour period to within 1 admission with 99% reliability?

When determining the sample size necessary for estimating the true population mean, which factor is not considered when sampling with replacement?

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 critical value for the 95% one-sided confidence interval for the proportion of students who skipped more than 10 days of school last year?

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 total market price of the houses in the suburban county constructed by the consulting group?

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, determine the sample size needed to estimate the proportion of managers who have caught salespeople working a second job on company time to within ±0.02 with 95% confidence.

A confidence interval was used to estimate the proportion of statistics students that are female. A random sample of 72 statistics students generated the following 90% confidence interval: (0.438, 0.642). Using the information above, what total size sample would be necessary if we wanted to estimate the true proportion to within ±0.08 using 95% confidence?

TABLE 8-3 A quality control engineer is interested in the mean length of sheet insulation being cut automatically by machine. The desired length of the insulation is 12 feet. It is known that the standard deviation in the cutting length is 0.15 feet. A sample of 70 cut sheets yields a mean length of 12.14 feet. This sample will be used to obtain a 99% confidence interval for the mean length cut by machine. -Referring to Table 8-3, the critical value to use in obtaining the confidence interval is______

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, the confidence interval obtained is valid only if the distribution of the population of salary offers is normal.

$\text { TABLE 8-5 }$ 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, a 95% confidence interval for the mean voltage of the power pack is wider than a 99% confidence interval.

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 the sample means will fall between 27.5 and 30.3.

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

TABLE 8-12 The president of a university is concerned that illicit drug use on campus is higher than the 5% acceptable level. A random sample of 250 students from a population of 2000 revealed that 7 of them had used illicit drug during the last 12 months. -Referring to Table 8-12, the president can be 90% confident that no more than 5% of the students at the university had used illicit drug during the last 12 months.

The standardized normal distribution is used to develop a confidence interval estimate of the population proportion when the sample size is sufficiently large.

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, 95% of the time, the proportion of people that recognize the product will fall between 0.36 and 0.54.

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, construct a 95% confidence interval estimate of the population proportion of managers who have caught salespeople working a second job on company time.

A race car driver tested his car for time from 0 to 60 mph, and in 20 tests obtained an average of 4.85 seconds with a standard deviation of 1.47 seconds. A 95% confidence interval for the 0 to 60 time is 4.52 seconds to 5.18 seconds.

Other things being equal, as the confidence level for a confidence interval increases, the width of the interval increases.