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Exam 8: Confidence Interval Estimation

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Question 51

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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. -True or False: 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.

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Question 52

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A confidence interval was used to estimate the proportion of statistics students who 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?

A) 105
B) 150
C) 420
D) 597

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Question 53

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TABLE 8-9 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." -True or False: Referring to Table 8-9,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.

TABLE 8-1 The managers of a company are worried about the morale of their employees.In order to determine if a problem in this area exists,they decide to evaluate the attitudes of their employees with a standardized test.They select the Fortunato test of job satisfaction,which has a known standard deviation of 24 points. -Referring to Table 8-1,they should sample ________ employees if they want to estimate the mean score of the employees within 5 points with 90% confidence.

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

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. -True or False: Referring to Table 8-8,a 99% confidence interval will contain 99% of the student population who own a personal computer.

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. -True or False: 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 8-11 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 8-11,what is the needed sample size to obtain a 90% confidence interval estimate of the percentage of the targeted young adults who will purchase the new game by allowing the same level of margin of error?

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, = 396 and S = 100.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?

TABLE 8-10 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,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 8-10,construct a 95% confidence interval estimate of the population proportion of managers who have caught salespeople giving a kickback to a customer.

True or False: 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 8-12 A random sample of 100 stores from a large chain of 500 garden supply stores was selected to determine the mean number of lawnmowers sold at an end-of-season clearance sale.The sample results indicated a mean of 6 and a standard deviation of 2 lawnmowers sold.A 95% confidence interval (5.623 to 6.377)was established based on these results. -True or False: Referring to Table 8-12,there are 10 possible samples of 100 stores that can be selected out of the population of 1,000 stores.

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, = 396 and S = 100.Which of the following assumptions is necessary in order for a confidence interval to be valid?

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 240 rooms.During February,a sample of 25 days has a sample mean of 370 rooms. -True or False: Referring to Table 8-7,a 90% confidence interval calculated from the same data would be narrower than a 99% confidence interval.

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. -True or False: Referring to Table 8-8,a 95% confidence interval for the proportion of the student population who own a personal computer is narrower than a 99% confidence interval.

TABLE 8-12 A random sample of 100 stores from a large chain of 500 garden supply stores was selected to determine the mean number of lawnmowers sold at an end-of-season clearance sale.The sample results indicated a mean of 6 and a standard deviation of 2 lawnmowers sold.A 95% confidence interval (5.623 to 6.377)was established based on these results. -True or False: Referring to Table 8-12,of all possible samples of 100 stores taken from the population of 1,000 stores,95% of the confidence intervals developed will contain the true population mean within the interval.

The head librarian at the Library of Congress has asked her assistant for an interval estimate of the mean number of books checked out each day.The assistant provides the following interval estimate: from 740 to 920 books per day.What is an efficient,unbiased point estimate of the number of books checked out each day at the Library of Congress?

True or False: The t distribution is used to develop a confidence interval estimate of the population proportion when the population standard deviation is unknown.

True or False: The t distribution allows the calculation of confidence intervals for means for small samples when the population variance is not known,regardless of the shape of the distribution in the population.

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 mean of the sample is ________,while the standard deviation of the sample is ________.