The state education commission wants to estimate the fraction of tenth grade students that have reading skills at or below the eighth grade level. In an earlier study, the population proportion was estimated to be 0.16.
How large a sample would be required in order to estimate the fraction of tenth graders reading at or below the eighth grade level at the 85% confidence level with an error of at most 0.03? Round your answer up to the next integer.
Using the data, construct the 80% confidence interval for the population proportion of new car buyers who prefer foreign cars over domestic cars. Round your answers to three decimal places.

A conservative investor would like to invest some money in a bond fund. The investor is concerned about the safety of her principal (the original money invested). Colonial Funds claims to have a bond fund which has maintained a consistent share price of $10. They claim that this share price has not varied by more than $0.25 on average since its inception. To test this claim, the investor randomly selects 24 days during the last year and determines the share price for the bond fund. The average share price of the sample is $11 with a standard deviation of $0.35. Assuming that the share prices of the bond fund have an approximately normal distribution, construct a 99% confidence interval for the standard deviation of the share price of the bond fund. Round any intermediate calculations to no less than six decimal places and round the endpoints of the interval to four decimal places.

Almost all smart devices (phones, tablets, and computers) are made with touch screens. A concern of many consumers is the shelf life of the “touch” component of the screens. A consumer advocacy group wanted to inform its members of a range that they can expect their touch screens to last. The group took a sample of 26 screens and measured the life of the “touch” function of the screens. That is, they used digital devices to simulate billions of touches to determine the life of the screens. Of the 26 screens sampled, the average “touch” life was 90 months with a standard deviation of seven months. Construct a 98% confidence interval for the standard deviation of the life of the touch screens. Assume that the life of the touch screens has an approximately normal distribution. Round any intermediate calculations to no less than six decimal places and round the endpoints of the interval to four decimal places.

The following sample of weights (in ounces) was taken from 12 boxes of crackers randomly selected from the assembly line.
17.65,16.11,16.71,17.01,17.14,16.3916.56,16.98,17.22,16.77,16.53,17.60
Construct a 98% confidence interval for the population variance for the weights of all boxes of crackers that come off the assembly line. Round to three decimal places.

A butcher uses a machine that packages ground beef in three-pound portions. A sample of 47 packages of ground beef has a standard deviation of 4.48 ounces. Construct a 99% confidence interval to estimate the standard deviation of the weights of all packages prepared by the machine. Round to two decimal places.