Exam 9: Confidence Intervals

The coffee and soup machine at the local subway station is supposed to fill cups with 6 ounces of soup. Ten cups of soup are bought with results of a mean of 5.93 ounces and a standard deviation of .13 ounces. How large a sample of soups would we need to be 95 percent confident that the sample mean is within .03 ounces of the population mean?

When the population is normally distributed and the population standard deviation σ is unknown, then for any sample size n, the sampling distribution of is based on the z distribution.

A sample of 100 items has a population standard deviation of 5.1 and a mean of 21.6. Construct a 95 percent confidence interval for μ.

Researchers have studied the role that the age of workers has in determining the hours per month spent on personal tasks. A sample of 1,686 adults were observed for one month. The data follow. Construct a 98 percent confidence interval for the mean hours spent on personal tasks for 25- to 44-year-olds.

What sample size is needed to obtain a 90 percent confidence interval for the mean protein content of meat if the estimate is to be within 2 pounds of the true mean value? Assume that the variance is 49 pounds.

A computer manufacturing company has sent a mail survey to 2,800 of its randomly selected customers that have purchased a new laptop. The survey asked the customers whether or not they were satisfied with the computer. Eight hundred customers responded to the survey: 640 customers indicated that they were satisfied, while 160 customers indicated they were not satisfied with their new computer. Construct a 96 percent confidence interval estimate of the true proportion of customers satisfied with their new computer.

If everything else is held constant, decreasing the margin of error causes the required sample size to ________.

First, a 90 percent confidence interval is constructed from a sample size of 100. Then, for the same identical data, a 92 percent confidence interval is constructed. The width of the 90 percent interval is wider than the 92 percent confidence interval.

When sample size is 11, find t_.025.

When solving for the sample size needed to compute a 95 percent confidence interval for a population proportion, p, having a given error bound, E, we choose a value of that makes (1 − ) as small as reasonably possible.

As the standard deviation (σ) decreases, the width of the confidence interval ________.

The width of a confidence interval will be

The U.S. Department of Health and Human Services collected sample data for 772 males between the ages of 18 and 24. That sample group has a mean height of 69.7 inches with a standard deviation of 2.8 inches. Find the 99 percent confidence interval for the mean height of all males between the ages of 18 and 24.

The quantity in the confidence intervals for μ and τ is called the finite population correction and is always less than 1.

If the 95 percent confidence interval for a mean is from .771 to 1.629, can we conclude that it is possible that μ = .5, using that 95 percent confidence interval?

Unoccupied seats on flights cause airlines to lose revenue. Suppose a large airline wants to estimate its average number of unoccupied seats per flight over the past year. Two hundred and twenty-five flight records are randomly selected, and the number of unoccupied seats is noted, with a sample mean of 11.6 seats and a standard deviation of 4.1 seats. How many flights should we select if we wish to estimate μ to within 2 seats and be 95 percent confident?

There is little difference between the values of t_α/2 and z_α/2 when

Health insurers and the federal government are both putting pressure on hospitals to shorten the average length of stay (LOS) of their patients. In 2003, the average LOS for non-heart patients was 4.6 days. A random sample of 20 hospitals in one state had a mean LOS for non-heart patients in 2008 of 3.8 days and a standard deviation of 1.2 days and is normally distributed. How large a sample of hospitals would we need to be 99 percent confident that the sample mean is within .5 days of the population mean?

When the level of confidence and sample proportion, , remain the same, a confidence interval for a population proportion, p, based on a sample of n = 100 will be wider than a confidence interval for p based on a sample of n = 400.

What is a 95 percent confidence interval for μ when n = 10, = 35.6, and s = 13.0? Assume population normality.