Exam 8: Sampling Distributions and Estimation

As n increases,the standard error decreases.

On the basis of a survey of 545 television viewers,a statistician has constructed a confidence interval and estimated that the proportion of people who watched the season premiere of Glee is between .16 and .24.What level of confidence did the statistician use in constructing this interval? Explain carefully,showing all steps in your reasoning.

If σ = 25,find the sample size to estimate the mean with an error of ±3 and 90 percent confidence (rounded to the next higher integer).

Concerning confidence intervals,which statement is most nearly correct?

To estimate a proportion with a 4 percent margin of error and a 95 percent confidence level,the required sample size is over 800.

The Central Limit Theorem can be applied to the sample proportion.

Last week,108 cars received parking violations in the main university parking lot.Of these,27 had unpaid parking tickets from a previous violation.Assuming that last week was a random sample of all parking violators,find the 95 percent confidence interval for the percentage of parking violators that have prior unpaid parking tickets.

In constructing a confidence interval for a mean,the width of the interval is dependent on the sample size,the confidence level,and the population standard deviation.

The standard deviation of the sample proportion p = x/n increases as n increases.

The owner of Limp Pines Resort wanted to know the average age of its clients.A random sample of 25 tourists is taken.It shows a mean age of 46 years with a standard deviation of 5 years.The width of a 98 percent CI for the true mean client age is approximately:

A financial institution wishes to estimate the mean balances owed by its credit card customers.The population standard deviation is $300.If a 99 percent confidence interval is used and an interval of ± $75 is desired,how many cardholders should be sampled?

Assuming that π = .50 is a quick and conservative approach to use in a sample size calculation for a proportion.

A 90 percent confidence interval will be wider than a 95 percent confidence interval,ceteris paribus.

When the sample standard deviation is used to construct a confidence interval for the mean,we would use the Student's t distribution instead of the normal distribution.

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

The Central Limit Theorem says that,if n exceeds 30,the population will be normal.

The standard error of the sample proportion does not depend on the confidence level.

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.

In a large lecture class,the professor announced that the scores on a recent exam were normally distributed with a range from 51 to 87.Using the Empirical Rule μ ± 3σ to estimate σ,how many students would you need to sample to estimate the true mean score for the class with 90 percent confidence and an error of ± 2?

An estimator must be unbiased if you are to use it for statistical analysis.