Exam 7: Estimation: Single Population

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: Suppose that the waiting times for patients at a local hospital are normally distributed with known population standard deviation of 30 minutes.A random sample of 75 patients in the local hospital had a mean time of 90 minutes.Assume a 95% confidence interval for the population mean μ. -Calculate the width of the 95% confidence interval estimate.

Keeping all other factors constant,the more the population standard deviation is reduced,the smaller the margin of error.

In order to estimate the average daily down time,a manufacturer randomly sampled 41 days of production records and found a mean of 51.75 minutes and standard deviation of 7.9 minutes.A 90% confidence interval for the population mean is:

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: A furniture mover calculates the actual weight as a proportion of estimated weight for a sample of 31 recent jobs.The sample mean is 1.13 and the sample standard deviation is 0.16. -Are the 95% confidence intervals for the population mean,using t tables and using the z table assuming that the population standard deviation is known to be 0.16,of roughly similar size? Explain.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: A process producing bricks is known to produce bricks whose weights are normally distributed with a standard deviation of 0.11 lb.A random sample of 16 bricks from today's output had a mean weight of 4.08 lb. -Find a 99% confidence interval for the mean weight of all bricks produced this day.

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. -Interpret what the 95% confidence interval estimate of the population mean tells you.

The number of bolts produced each hour from a particular machine is normally distributed with a standard deviation of 7.4.For a random sample of 15 hours,the average number of bolts produced was 587.3.Find the upper and lower confidence limits of a 98% confidence interval for the population mean number of bolts produced per hour.

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): -Calculate the sample mean.

The number of television sets produced from an assembly line each day is known to have a standard deviation of 17.4 sets per day.The production line averaged 452.3 sets per day for 20 randomly selected days.Which of the following represents a 95% confidence interval for the population mean number of sets per hour?

Interval estimates for the variance of a normal population rely on the random variable (n - 1)s² / σ²,which follows:

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: Suppose that the waiting times for patients at a local hospital are normally distributed with known population standard deviation of 30 minutes.A random sample of 75 patients in the local hospital had a mean time of 90 minutes.Assume a 95% confidence interval for the population mean μ. -What is the formula used to calculate the standard error?

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: A Monte Carlo study involves 10,000 random samples of size 20 from a normal population with mean μ = 120 and standard deviation σ = 20.For each sample,the mean and the median are calculated,with the following results: -What does the study suggest about the bias of the estimators in this situation?

If a sample has 20 observations and a 90% confidence estimate for μ is needed,the appropriate t-score is:

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): -The number of television sets coming off a production line each day is known to have a standard deviation of 118.5 sets per day.The production manager tells you that the 90% confidence interval for the population mean was 552.3 to 621.9.How large a sample was this confidence interval based on?

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. -Check for evidence of nonnormality.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: A process producing bricks is known to produce bricks whose weights are normally distributed with a standard deviation of 0.11 lb.A random sample of 16 bricks from today's output had a mean weight of 4.08 lb. -Without doing the calculations,explain whether a 95% confidence interval for the mean weight of all bricks produced this day would be wider than,narrower than,or the same width as that of a 99% confidence interval.

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. -Give a careful verbal interpretation of the 95% confidence interval for the long-run proportion of new product placements.

A point estimator ₁ is said to be more efficient than a point estimator ₂ if Var( ₁)> Var( ₂).

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: A furniture mover calculates the actual weight as a proportion of estimated weight for a sample of 31 recent jobs.The sample mean is 1.13 and the sample standard deviation is 0.16. -Calculate a 95% confidence interval for the population mean using t tables.

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 + 0.40 X₂ + 0.40 X₃ + 0.10 X₄ and ₂ = 0.20 X₁ + 0.30 X₂ + 0.30 X₃ + 0.20 X₄ -Which of the following constraints is true?