Exam 7: Estimation: Single Population

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: The number of beverage cans produced each hour from a vending machine is normally distributed with a standard deviation of 8.6.For a random sample of 12 hours,the average number of beverage cans produced was 326.0.Assume a 99% confidence interval for the population mean number of beverage cans produced per hour. -Calculate the width of the 99% confidence interval estimate.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: The sales manager for a hardware wholesaler finds that 229 of the previous 500 calls to hardware store owners resulted in new product placements.Assume that the 500 calls represent a random sample. -Find the confidence interval for estimating the population proportion for 90% confidence level;sample size n = 675;and sample proportion = 0.10.

You are interested in determining the amount of time (in minutes)you spend each day on the Internet.For seven days,these values are: 51,24,16,88,63,28,and 59.Assume that the amount of time you spend on the Internet each day is normally distributed,and develop a 90% confidence interval for the population average amount of time.

What is the relative efficiency of Z with respect to Y?

The maximum distance between an estimator and the true value of a parameter is called the margin of error.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: A random sample of ten homes in a particular suburb had the following selling prices (in thousands of dollars): 92,83,110,115,108,96,102,90,100,and 98. -Use an unbiased estimator to estimate the proportion of homes in this suburb selling for less than $95,000.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: Let X₁,X₂,X₃,and X₄ be a random sample of observations from a population with mean μ and variance σ².Consider the following two point estimators of μ: ₁ = 0.10 X₁ + 0.20 X₂ + 0.40 X₃ + 0.30 X₄,and ₂ = 0.25 X₁ + 0.25 X₂ + 0.30 X₃ + 0.20 X₄ -Show that both the estimators are unbiased.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: Let X₁,X₂,X₃,and X₄ be a random sample of observations from a population with mean μ and variance σ².Consider the following two point estimators of μ: ₁ = 0.10 X₁ + 0.20 X₂ + 0.40 X₃ + 0.30 X₄,and ₂ = 0.25 X₁ + 0.25 X₂ + 0.30 X₃ + 0.20 X₄ -Find the relative efficiency of ₂ with respect to ₁

What is the relative efficiency of W with respect to X?

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: The data shown below specify how much a sample of 20 executives paid in federal income taxes,as a percentage of gross income,are reproduced below. Assume that the standard deviation for the underlying population is equal to 4.0. -Calculate a 95% confidence interval for the population mean.

The sample proportion is a biased estimator of the population proportion P.

A narrower confidence interval for a population parameter with a given confidence level can be obtained by increasing the sample size.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: Suppose that the amount of time teenagers spend on the internet is normally distributed with a standard deviation of 1.5 hours.A sample of 100 teenagers is selected at random,and the sample mean is computed as 6.5 hours. -Determine the 95% confidence interval estimate of the population mean.

Find the upper confidence limit of the 95% confidence interval.

The following sample was taken from a normally distributed population: 20,27,15,20,16,22,and 13.A 95% confidence interval for the population mean using this sample is:

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: The data shown below specify how much a sample of 20 executives paid in federal income taxes,as a percentage of gross income,are reproduced below. Assume that the standard deviation for the underlying population is equal to 4.0. -Closed caption movies allow the hearing impaired to enjoy the dialogue as well as the acting.A local organization for the hearing impaired people of the community takes a random sample of 100 movie listings offered by the cable television company in order to estimate the proportion of closed caption movies offered.They observed that 14 movies were closed caption.The cable television company says at least 5% of the movies shown are closed captioned.Prepare a 90% confidence interval for the true proportion P and comment on the cable television company's claim.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: A regional CPA firm conducted an audit for a discount chain.One part of the audit involved developing an estimate for the mean dollar error in total charges that occur during the checkout process.They wish to develop a 90% confidence interval estimate for the population mean.A simple random sample of n = 20 is selected,with the following data (in dollars): -There is concern about the speed of automobiles traveling over US 131.For a random sample of seven automobiles radar indicated the following speeds,in miles per hour: 80,74,69,78,87,72,and 70.Assuming a normal population distribution,find the margin of error of a 95% confidence interval for the mean speed of all automobiles traveling over this stretch of highway.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: A researcher is interested in determining the percentage of all households in the U.S.that have more than one home computer.In a survey of 492 households,27% indicated that they own more than one home computer. -Develop a 90% confidence interval for the proportion of all households in the U.S.with more than one computer.

If the population is normally distributed,both the sample mean and the median are unbiased estimators of the population mean.

The manager of the local health club is interested in determining the number of times members use the weight room per month.She takes a random sample of 15 members and finds that over the course of a month,the average number of visits was 11.2 with a standard deviation of 3.2.Assuming that the monthly number of visits is normally distributed,which of the following represents a 95% confidence interval for the average monthly usage of all health club members?