Exam 8: Confidence Interval Estimation

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.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 8-8 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 ________.

In estimating the population mean with the population standard deviation unknown,if the sample size is 12,there will be 6 degrees of freedom.

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 sampling error is 3%.

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 listing a "strip bar" as a restaurant on an expense report.

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 will contain 99% of the student population who own a personal computer.

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 99% confidence interval for the mean number of rooms rented daily in a given month is 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,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 ________.

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?

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

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 for the proportion of the student population who feel comfortable reporting cheating by their fellow students is from ________ to ________.

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,this interval requires the assumption that the distribution of the number of people recognizing the product has a normal distribution.

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 confidence interval estimate of the population proportion would only be valid if the distribution of the number of students who feel comfortable reporting cheating by their fellow students is normal.

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?

A sample size of 5 provides a sample mean of 9.6.If the population variance is known to be 5 and the population distribution is assumed to be normal,the lower limit for a 90% confidence interval is 7.96.

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 entire population.

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

TABLE 8-8 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 mean number of students in the 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,the sampling error of a 95% confidence interval estimate of the population proportion of managers who have caught salespeople working a second job on company time is ________.

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