Exam 8: Confidence Interval Estimation

SCENARIO 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 Scenario 8-8,we are 99% confident that between 79.11% and 87.69% of the student population own a personal computer.

SCENARIO 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 Scenario 8-4,a 99% confidence interval will contain 99% of the voltages for all such power packs.

The width of a confidence interval equals twice the sampling error.

SCENARIO 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 Scenario 8-4,it is possible that the 99% confidence interval calculated from the data will not contain the mean voltage for the entire population.

SCENARIO 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 Scenario 8-3,for the confidence interval to be valid,it is necessary that test scores of students in the special study program on the actuarial exam be normally distributed.

Other things being equal,as the confidence level for a confidence interval increases,the width of the interval increases.

A university dean is interested in determining the proportion of students who receive some sort of financial aid.Rather than examine the records for all students,the dean randomly selects 200 students and finds that 118 of them are receiving financial aid.If the dean wanted to estimate the proportion of all students receiving financial aid to within 3% with 99% reliability,how many students would need to be sampled?

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 normal,what is the shape of the sampling distribution of the sample mean that will be used to create the desired confidence interval for ? ?

SCENARIO 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. -Referring to Scenario 8-7,a 90% confidence interval calculated from the same data would be narrower than a 99% confidence interval.

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

SCENARIO 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 Scenario 8-3,the confidence interval will be based on _____degrees of freedom.

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_____ .

The t distribution is used to develop a confidence interval estimate of the population mean when the population standard deviation is unknown.

A population parameter is used to estimate a confidence interval.

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

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?

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

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

SCENARIO 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 Scenario 8-5,95% of the salary offers are between 47.19 and 52.61.

Suppose a 95% confidence interval for μ turns out to be (1,000,2,100).To make more useful inferences from the data,it is desired to reduce the width of the confidence interval.Which of the following will result in a reduced interval width?