Exam 8: Confidence Interval Estimation

TABLE 8-13 A sales and marketing management magazine conducted a survey of salespeople cheating on their expense reports and other unethical conduct. In the survey of 200 managers, 58% of the managers have caught salespeople cheating on an expense report, 50% have caught salespeople working a second job on company time, 22% have caught salespeople listing a "strip bar" as a restaurant on an expense report, and 19% have caught salespeople giving a kickback to a customer. -Referring to Table 8-13, 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.

TABLE 8-6 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. -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. Suppose there is no information about the proportion of students who might choose the option. 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?

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

TABLE 8-12 The president of a university is concerned that the percentage of students who have cheated on an exam is higher than the 1% acceptable level. A confidential random sample of 1,000 students from a population of 7,000 revealed that 6 of them said that they had cheated on an exam during the last semester. -Referring to Table 8-12, using the 90% one-sided confidence interval, the superintendent can be 85% confident that no more than 1% of the students at the university had cheated on an exam during the last semester.

In forming a 90% confidence interval for a population mean from a sample size of 22, the number of degrees of freedom from the t distribution equals 22.

A point estimate consists of a single sample statistic that is used to estimate the true population parameter.

TABLE 8-11 A university wanted to find out the percentage of students who felt comfortable reporting cheating by their fellow students. A survey 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 8-11, it is possible that the 99% confidence interval calculated from the data will not contain the sample proportion of students who feel comfortable reporting cheating by their fellow students.

TABLE 8-8 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 8-8, it is possible that the 99% confidence interval calculated from the data will not contain the sample proportion of students who own a personal computer.

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 confidence interval will be obtained for the proportion of cases of recidivism. Part of this calculation includes the estimated standard error of the sample proportion. For this sample, the estimated standard error is ________.

TABLE 8-3 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 8-3, the critical value used in constructing a 90% confidence interval is ________.

For a given data set, the confidence interval will be wider for 95% confidence than for 90% confidence.

TABLE 8-7 A hotel chain wants to estimate the mean number of rooms rented daily in a given month. The population of rooms rented daily is assumed to be normally distributed for each month with a standard deviation of 24 rooms. During February, a sample of 25 days has a sample mean of 37 rooms. -Referring to Table 8-7, a 95% confidence interval for the mean number of rooms rented daily in a given month is narrower than a 99% confidence interval.

TABLE 8-14 A poll was conducted by the marketing department of a video game company to determine the popularity of a new game that was targeted to be launched in three months. Telephone interviews with 1,500 young adults were conducted which revealed that 49% said they would purchase the new game. The margin of error was ±3 percentage points. -Referring to Table 8-14, what is the needed sample size to obtain a 95% confidence interval in estimating the percentage of the targeted young adults who will purchase the new game to within ±5%?

TABLE 8-8 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 8-8, the parameter of interest is the proportion of the student population who own a personal computer.

TABLE 8-13 A sales and marketing management magazine conducted a survey of salespeople cheating on their expense reports and other unethical conduct. In the survey of 200 managers, 58% of the managers have caught salespeople cheating on an expense report, 50% have caught salespeople working a second job on company time, 22% have caught salespeople listing a "strip bar" as a restaurant on an expense report, and 19% have caught salespeople giving a kickback to a customer. -Referring to Table 8-13, it is possible that the 95% confidence interval calculated from the data will not contain the population proportion of managers who have caught salespeople cheating on an expense report.

TABLE 8-13 A sales and marketing management magazine conducted a survey of salespeople cheating on their expense reports and other unethical conduct. In the survey of 200 managers, 58% of the managers have caught salespeople cheating on an expense report, 50% have caught salespeople working a second job on company time, 22% have caught salespeople listing a "strip bar" as a restaurant on an expense report, and 19% have caught salespeople giving a kickback to a customer. -Referring to Table 8-13, we are 95% confident that the population mean number of managers who have caught salespeople cheating on an expense report is between 0.5116 to 0.6484.

TABLE 8-13 A sales and marketing management magazine conducted a survey of salespeople cheating on their expense reports and other unethical conduct. In the survey of 200 managers, 58% of the managers have caught salespeople cheating on an expense report, 50% have caught salespeople working a second job on company time, 22% have caught salespeople listing a "strip bar" as a restaurant on an expense report, and 19% have caught salespeople giving a kickback to a customer. -Referring to Table 8-13, we are 95% confident that between 51.16% and 64.84% of managers in the population have caught salespeople cheating on an expense report.

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, the critical value of t will be

When determining the sample size for a proportion for a given level of confidence and sampling error, the closer to 0.50 that π is estimated to be, the sample size required ________.

The standardized normal distribution is used to develop a confidence interval estimate of the population proportion regardless of whether the population standard deviation is known.