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, the sampling error of a 99% confidence interval for the proportion of the student population who own a personal computer is __________.

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

When determining the sample size for a proportion for a given level of confidence and sampling error, the closer to 0.50 that is estimated to be, the sample size required __________.

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 99% confidence interval will contain 99% of the sample mean number of rooms rented daily in a given month.

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

SCENARIO 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 Scenario 8-6, 95% of the time, the sample proportion of people that recognize the product will fall between 0.36 and 0.54.

SCENARIO 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". -Referring to Scenario 8-9, it is possible that the 99% confidence interval calculated from the data will not contain the sample proportion of students who feel comfortable reporting cheating by their fellow students.

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

The confidence interval estimate of the population mean is constructed around the sample mean.

SCENARIO 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 Scenario 8-6, 95% of the people will recognize the product between 36% and 54% of the time.

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, it is possible that the 99% confidence interval calculated from the data will not contain the sample mean number of rooms rented daily in a given month.

SCENARIO 8-1 The managers of a company are worried about the morale of their employees.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 Scenario 8-1, they should sample ________ employees if they want to estimate the mean score of the employees within 5 points with 90% confidence.

Private colleges and universities rely on money contributed by individuals and corporations for their operating expenses.Much of this money is put into a fund called an endowment, and the college spends only the interest earned by the fund.A recent survey of 8 private colleges in the United States revealed the following endowments (in millions of dollars): 60.2, 47.0, 235.1, 490.0, 122.6, 177.5, 95.4, and 220.0.Summary statistics yield and S = 143.042 .Calculate a 95% confidence interval for the mean endowment of all the private colleges in the United States assuming a normal distribution for the endowments.

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, Which of the following assumptions is necessary for a confidence interval to be valid?

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

SCENARIO 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 Scenario 8-11, 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% if you do no t have the information on the 49% in the interviews who said that they would purchase the new game?

A race car driver tested his car for time from 0 to 60 mph, and for 20 tests obtained a mean of 4.85 seconds with a standard deviation of 1.47 seconds.A 95% confidence interval for the 0 to 60 mean time is 4.52 seconds to 5.18 seconds.

An economist is interested in studying the incomes of consumers in a 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 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: and S = 20 .Construct a 95% confidence interval for the mean amount its credit card customers spent on their first visit to the chain's new store in the mall if the amount spent follows a normal distribution.

The sample mean is a point estimate of the population mean.