Out of 159 randomly selected adults in the United States who were surveyed, 81 exercise on a regular basis. Construct a 90% confidence interval for the proportion of all adults in the United States who exercise on a regular basis. Round 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.

A hospital would like to determine the mean length of stay for its patients having abdominal surgery. A sample of 17 patients revealed a sample mean of 5.7 days and a sample standard deviation of 1.6 days. Assume that the lengths of stay are approximately normally distributed. Find a 95% confidence interval for the mean length of stay for patients with abdominal surgery. Round the endpoints to two decimal places, if necessary.

A survey of several 10 to 13 year olds recorded the following amounts spent on a trip to the mall:
$19.54,$21.01,$19.37 Construct the 98% confidence interval for the average amount spent by 10 to 13
year olds on a trip to the mall. Assume the population is approximately normal.
a. Calculate the sample mean for the given sample data. Round your answer to two decimal places.
b. Calculate the sample standard deviation for the given sample data. Round your answer to two decimal places.
c. Find the critical value that should be used in constructing the confidence interval. Round your answer to three decimal places.
d. Construct the 98% confidence interval. Round your answer to two 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.