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.

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 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.

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.