Exam 10: Introduction to Estimation

The width of the confidence interval estimate of the population mean $\mu$ is a function of only two quantities: the population standard deviation $\sigma$ and the sample size n.

An interval estimator estimates the value of an unknown ____________________.

In determining the size n needed to estimate the population mean, n increases as the confidence level decreases.

An unbiased estimator is a sample statistic whose expected value equals the population parameter.

Which of the following statements is true?

If the population standard deviation is guesstimated, and it turned out to be smaller than you assumed, then the sample size you calculated is ____________________ than it needs to be.

A point estimator is defined as:

One can reduce the width of a confidence interval by taking a smaller sample size.

Draw the sampling distribution of two unbiased estimators for $\mu$ , one of which is relatively efficient.

In this chapter you need four values to construct the confidence interval estimate of $\mu$ .They are the sample mean, the sample size, the population standard deviation, and the confidence level.

If the confidence level is reduced, the confidence interval:

In determining the sample size n needed to estimate the population mean, n decreases as the desired width of the confidence interval decreases.

A sample of 49 measurements of tensile strength for roof hangers are calculated to have a mean of 2.45 and a standard deviation of 0.25.(Units are Newton's per square meter.) a. Determine the 95% confidence interval for mean tensile strength for all hangers. b. Interpret this confidence interval.

The larger the confidence level used in constructing a confidence interval estimate of the population mean, the narrower the confidence interval.

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

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 90% confidence interval estimate of the population mean.

In the formula for a confidence interval for $\mu$ , 1 - $\alpha$ is called the ____________________.

As the bound on the error of estimation decreases, the sample size ____________________.

The sampling error for a confidence interval is also defined as the ____________________ of ____________________.

College Dean A college dean would like to estimate a population mean to within 40 units with 99% confidence given that the population standard deviation is 200. -{College Dean Narrative} What sample size should be used if the standard deviation is changed to 50?