91Ó°ÊÓ

Assume that the population standard deviation is known and decide weather use of the $z$interval procedure to obtain a confidence interval for the population mean is reasonable. Explain your answers.

The variable under consideration is very close to being normally distributed, and the sample size is$75$.

Express the form of most of the confidence intervals that you will encounter in your study of statistics in terms of "point estimate" and "margin of error."

Explain the effect on the margin of error and hence the effect on the accuracy of estimating a population mean by a sample mean.

Decreasing the confidence level while keeping the same sample size.

A confidence interval for a population mean has a margin of error of $0.047$

a. Determine the length of the confidence interval.

b. If the sample mean is $0.205$, obtain the confidence interval.

c. Construct a graph that illustrates your results.

Suppose that you take$500$ simple random samples from a population and that, for each sample, you obtain a $90\%$confidence interval for an unknown parameter. Approximately how many of those confidence intervals will not contain the value of the unknown parameter?

State True or False. Give Reasons for your answers.

The confidence level can be determined if you know only the margin of error, population standard deviation, and sample size.

Political Prisoners. A. Ehlers et al. studied various characteristics of political prisoners from the former East Germany and presented their findings in the paper "Posttraumatic Stress Disorder (PTSD) Following Political Imprisonment: The Role of Mental Defeat. Alienation, and Perceived Permanent Change". According to the article. the mean duration of imprisonment for 32 patients with chronic PTSD was $33.4$months. Assuming that $\mathrm{σ}=42$months, determine a $95\%$confidence interval for the mean duration of imprisonment,$\mathrm{μ}$. of all East German political prisoners with chronic PTSD. Interpret your answer in words.

Keep on Rolling. The Rolling Stones, a rock group formed in the $1960\mathrm{s}$, have toured extensively in support of new albums, Pollstar has collected data on the earnings from the Stones's North American tours. For thirty randomly selected Rolling Stones concerts, the mean gross earnings is $\backslash (2.27$ million. Assuming a population standard deviation gross earnings of $\backslash )0.5$ million, obtain a $99\%$ confidence interval for the mean gross earnings of all Rolling Stones concerts. Interpret your answer in words.

A simple random sample is taken from a population and yields the following data for a variable of the population:

Find a point estimate for the population mean (i.e., the mean of the variable).