Exam 8: Confidence Interval Estimation

TABLE 8-4 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 8-4, it is possible that the 99% confidence interval calculated from the data will not contain the mean voltage for the sample.

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, a 99% confidence interval for the proportion of the student population who own a personal computer is from ________ to ________.

TABLE 8-5 A sample of salary offers (in thousands of dollars) given to management majors is: 48, 51, 46, 52, 47, 48, 47, 50, 51, and 59. Using this data to obtain a 95% confidence interval resulted in an interval from 47.19 to 52.61. -Referring to Table 8-5, 95% of the salary offers are between 47.19 and 52.61.

The difference between the sample proportion and the population proportion is called the sampling error.

It is desired to estimate the mean total compensation of CEOs in the Service industry. Data were randomly collected from 18 CEOs and the 95% confidence interval was calculated to be ($2,181,260, $5,836,180). Which of the following interpretations is correct?

TABLE 8-4 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 8-4, a 90% confidence interval calculated from the same data would be narrower than a 99% confidence interval.

A random sample of 50 provides a sample mean of 31 with a standard deviation of S = 14. The upper bound of a 90% confidence interval estimate of the population mean is 34.32.

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

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, a 99% confidence interval will contain 99% of the student population who feel comfortable reporting cheating by their fellow students.

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, the sampling error of a 95% confidence interval estimate of the population proportion of managers who have caught salespeople cheating on an expense report is ________.

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.

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, the standard error is 3%.

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

A major department store chain is interested in estimating the mean 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 S = 20. 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?

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 total sample size would the economist need to use for a 95% confidence interval if the width of the interval should not be more than $100?

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 8-13 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, construct a 95% confidence interval estimate of the population proportion of managers who have caught salespeople working a second job on company time.

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. -Referring to Table 8-6, it is possible that the true proportion of people that recognize the product is between 0.36 and 0.54.

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, we are 99% confident that the average number of rooms rented daily in a given month is somewhere between 24.64 and 49.36.

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 ________.