Exam 8: Sampling Distributions and Estimation

We could narrow a 95 percent confidence interval by:

As long as the sample is more than one item, the standard error of the sample mean will be smaller than the standard deviation of the population.

To narrow the confidence interval for π, we can either increase n or decrease the level of confidence.

The Student's t distribution is always symmetric and bell-shaped, but its tails lie above the normal.

For a sample size of 20, a 95 percent confidence interval using the t distribution would be wider than one constructed using the z distribution.

The confidence interval half-width when π = .50 is called the margin of error.

The sample mean is not a random variable when the population parameters are known.

The standard error of the mean decreases when:

Based on the Rule of Three, if no events occur in n independent trials we can set the upper 95 percent confidence bound at 3/n.

A higher confidence level leads to a narrower confidence interval, ceteris paribus.

A highway inspector needs an estimate of the mean weight of trucks crossing a bridge on the interstate highway system. She selects a random sample of 49 trucks and finds a mean of 15.8 tons with a sample standard deviation of 3.85 tons. The 90 percent confidence interval for the population mean is:

Which of the following statements is most nearly correct, other things being equal?

A random sample of 160 commercial customers of PayMor Lumber revealed that 32 had paid their accounts within a month of billing. Can normality be assumed for the sample proportion?

Why does σ pose a problem for sample size calculation for a mean? How can σ be approximated when it is unknown?

Professor York randomly surveyed 240 students at Oxnard University and found that 150 of the students surveyed watch more than 10 hours of television weekly. How many additional students would Professor York have to sample to estimate the proportion of all Oxnard University students who watch more than 10 hours of television each week within ± 3 percent with 99 percent confidence?

For a given sample size, the higher the confidence level, the:

The owner of Torpid Oaks B&B wanted to know the average distance its guests had traveled. A random sample of 16 guests showed a mean distance of 85 miles with a standard deviation of 32 miles. The 90 percent confidence interval (in miles) for the mean is approximately:

Read the news story below. Using the 95 percent confidence level, what sample size would be needed to estimate the true proportion of stores selling cigarettes to minors with an error of ± 3 percent? Explain carefully, showing all steps in your reasoning. $\quad$$\quad$$\quad$ Decoys Catch Stores in Cigarette-Sale Sting The Tri-Cities Tobacco Reduction coalition recently sent three underage teenagers out to see whether they could buy cigarettes from stores in Detroit and Highland Park. The results were not good. Of the 320 stores checked, 82 sold cigarettes to the teens, who were between the ages of 15 and 17. People must be 18 to legally buy cigarettes in Michigan. When the age of the buyer is not clear, the retailer is supposed to check the buyer's ID. The stores that sold the cigarettes will face fines. Source: Detroit Free Press, March 19, 2001, p. 2C.

Which of the following is not a characteristic of the t distribution?

To estimate π, you typically need a sample size equal to at least 5 percent of your population.