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,a 99% confidence interval will contain 99% of the voltages for all such power packs.

The county clerk wants to estimate the proportion of voters who will need special election facilities.Suppose a sample of 400 voters was taken.If 150 need special election facilities,calculate a 90% confidence interval for the population proportion.

Suppose a 95% confidence interval for μ turns out to be (1,000,2,100).Give a definition of what it means to be "95% confident" as an inference.

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%?

Sampling error equals half the width of a confidence interval.

TABLE 8-10 The president of a university is concerned that illicit drug use on campus is higher than the 5% targeted level.A random sample of 250 students from a population of 2,000 revealed that 7 of them had used illicit drugs during the last 12 months. -Referring to Table 8-10,using the 90% one-sided confidence interval,the president can be 85% confident that no more than 5% of the students at the university had used illicit drugs during the last 12 months.

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?

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 confidence interval will be based on ________ degrees of freedom.

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.If the head librarian knows that the population standard deviation is 150 books checked out per day,approximately how large a sample did her assistant use to determine the interval estimate?

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,we are 99% confident that the total numbers of the student population who feel comfortable reporting cheating by their fellow students is between 0.4557 and 0.5043.

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,the president can be 90% confident that no more than 1% of the students at the university had cheated on an exam during the last semester.

Given a sample mean of 2.1 and a population standard deviation of 0.7 from a sample of 10 data points,a 90% confidence interval will have a width of 2.36.

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

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 8-5 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 sample means will fall between 47.19 and 52.61.

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,we are 99% confident that between 79.11% and 87.69% of the student population 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,what is the needed sample size to obtain a 95% 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?

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 between 24.64% and 49.36% of the rooms will be rented daily in a given month.

A quality control engineer is interested in estimating the proportion of defective items coming off a production line.In a sample of 300 items,27 are defective.A 90% confidence interval for the proportion of defectives from this production line would go from ________ to ________.

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 ________.