Chapter 8: Confidence Intervals for One Population Mean

Find the confidence level and $\propto$ for

a. $90\%$confidence interval.

b. $94\%$confidence interval.

Fuel Economy. The U.S. Department of Energy collects fuel economy information on new motor vehicles and publishes its findings in Fuel Economy Guide. The data included are the result of vehicle testing done at the Environmental Protection Agency's National Vehicle and Fuel Emissions Laboratory in Ann Arbor, Michigan, and by vehicle manufacturers themselves with oversight by the Environmental Protection Agency. On the Weiss Stats site, we provide the highway mileages, in miles per gallon (mpg), for one year's cars. Use the technology of your choice to do the following.

a. Obtain a random sample of $35$ of the mileages.

b. Use your data from part (b) and the $t-$interval procedure to find a $95\%$ confidence interval for the mean highway gas mileage of all cars of the year in question.

c. Does the mean highway gas mileage of all cars of the year in question lie in the confidence interval that you found in part (c)? Would it necessarily have to? Explain your answers.

Find the confidence level and $\alpha$for

a. $85\%$confidence interval.

b. $95\%$confidence interval

Old Faithful Geyser. In the online article "Old Faithful at Yellowstone, a Bimodal Distribution," D. Howell examined various aspects of the Old Faithful Geyser at Yellowstone National Park. Despite its name, there is considerable variation in both the length of the eruptions and in the time interval between eruptions. The times between eruptions, in minutes, for $500$ recent observations are provided on the Weiss Stats site.

a. Identify the population and variable under consideration.

b. Use the technology of your choice to determine and interpret a $99\%$ confidence interval for the mean time between eruptions.

c. Discuss the relevance of your confidence interval for future eruptions, say, $5$ years from now.

What is meant by saying that a $1-\alpha$confidence interval is

a. exact?

b. approximately correct?

Answer true or false to the following statement, and give a reason for your answer: If a $95\%$ confidence interval for a population mean. $\mathit{\mu }$, is from $33.8$ to $39.0$, the mean of the population must lie somewhere between $33.8$ and $39.0$

When estimating an unknown parameter, what does the margin of error indicate?

In developing Procedure $8.1$we assumed that the variable under consideration is normally distributed.

a. Explain why we needed that assumption.

b. Explain why the procedure yields an approximately correct confidence interval for large samples, regardless of the distribution of the variable under consideration.

For what is normal population an abbreviation?

Refer to Procedure $8.1.$

a. Explain in detail the assumptions required for using the $z-$interval procedure.

b. How important is the normality assumption? Explain your answer.