Exam 10: Introduction to Estimation

The temperature readings for 20 fall days (degrees Fahrenheit) in Wheeling, West Virginia, are normally distributed with a mean of 5.5 degrees and a standard deviation of 1.5 degrees.Determine the 90% confidence interval estimate for the fall mean temperature.

A confidence interval is an interval estimate for which there is a specified degree of certainty that the actual value of the population parameter will fall within the interval.

Which of the following conditions does not allow you to use the formula to estimate $\mu$ ?

An interval estimate is an estimate of the range for a sample statistic.

In developing an interval estimate for a population mean, the population standard deviation $\sigma$ was assumed to be 10.The interval estimate was 50.92 2.14.Had $\sigma$ equaled 20, the interval estimate would be

It is ____________________ to say that a 95% confidence interval means there is a 95% chance that the parameter lies in that confidence interval.

The width of a 95% confidence interval is 0.95.

Time Spent Playing Computer Games Suppose that the amount of time teenagers spend playing computer games per week is normally distributed with a standard deviation of 1.5 hours.A sample of 100 teenagers is selected at random, and the sample mean computed as 6.5 hours. -{Time Spent Playing Computer Games Narrative} Determine the 95% confidence interval estimate of the population mean if the sample size is changed to 300.

A market researcher is interested in studying the incomes of consumers in a particular region.The population standard deviation is known to be $1,000.A random sample of 50 individuals resulted in an average income of $15,000.What is the upper end point in a 99% confidence interval for the average income?

Is the sample mean a consistent estimator of the population mean? Explain

Time Spent Playing Computer Games Suppose that the amount of time teenagers spend playing computer games per week is normally distributed with a standard deviation of 1.5 hours.A sample of 100 teenagers is selected at random, and the sample mean computed as 6.5 hours. -{Time Spent Playing Computer Games Narrative} Determine and interpret the 99% confidence interval estimate of the population mean.

A random sample of 10 waiters in Weston, West Virginia, revealed the following hourly earnings, including tips: 19, 18, 15, 16, 18, 17, 16, 18, 20, and 14.(Units are dollars.) a. If the hourly earnings are normally distributed with a standard deviation of $4.50, estimate with 95% confidence the mean hourly earnings for all waitresses in Iowa City. b. Interpret your confidence interval.

After constructing a confidence interval estimate for a population mean, you believe that the interval is useless because it is too wide.In order to correct this problem, you need to:

Suppose that a 90% confidence interval for $\mu$ is given by .This notation means that we are 90% confident that $\mu$ falls between and .

If the population values are very close to each other, the width of the confidence interval is ____________________ than if the population values are very far apart.

The bound on the error of estimation is the ____________________ amount of sampling error that we are willing to tolerate.

Define unbiasedness.

In order to construct a confidence interval estimate of the population mean, the value of the population mean is needed.

If there are two unbiased estimators of a parameter, the one whose variance is smaller is said to be relatively efficient.

Suppose that a 95% confidence interval for $\mu$ is given by .This notation means that, if we repeatedly draw samples of the same size from the same population, 95% of the values of will be such that $\mu$ would lie somewhere between and .