Exam 9: Confidence Intervals

When the population is normally distributed, population standard deviation σ is unknown, and the sample size is n = 15, the confidence interval for the population mean μ is based on

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. Construct a 95.44 percent tolerance interval of the machine-fill amounts and a 95 percent confidence interval for the true machine-fill amount.

A local company makes a candy that is supposed to weigh 1.00 ounces. A random sample of 25 pieces of candy produces a mean of .996 ounces with a standard deviation of .004 ounces. Construct a 98 percent confidence interval for the mean weight of all such candy.

When the level of confidence and the sample size remain the same, a confidence interval for a population mean, μ, will be wider when the sample standard deviation, s, is small than when s is large.

When determining the sample size (n) for a confidence interval for ρ, if past experience tells us that p is at least .8, use p = .2.

Recently, a case of food poisoning was traced to a particular restaurant chain. The source was identified, and corrective actions were taken to make sure that the food poisoning would not reoccur. Despite the response from the restaurant chain, many consumers refused to visit the restaurant for some time after the event. A survey was conducted three months after the food poisoning occurred, with a sample of 319 former customers contacted. Of the 319 contacted, 29 indicated that they would not go back to the restaurant because of the potential for food poisoning. Construct a 95 percent confidence interval for the true proportion of the market who still refuse to visit any of the restaurants in the chain three months after the event.

A tolerance interval is meant to contain a specified percentage of the individual population measurements.

When the margin of error is added to and subtracted from the sample mean, an interval is formed that will contain μ with a probability of (1 − α).

A cable TV company wants to estimate the percentage of cable boxes in use during an evening hour. An approximation is 20 percent. They want the estimate to be at the 90 percent confidence level and within 2 percent of the actual proportion. What sample size is needed?

When constructing a confidence interval for a sample proportion, the t distribution is appropriate if the sample size is small.

When the level of confidence and sample size remain the same, a confidence interval for a population proportion, p, will be ________ when (1 − ) is larger than when (1 − ) is smaller.

When determining the sample size (n) for a confidence interval for ρ, if you have no idea what value p is (it could be any value between 0 and 1), use p = .5.

When the level of confidence and the sample size remain the same, a confidence interval for a population mean μ will be ________ when the sample standard deviation s is small than when s is large.

A random sample n = 15 is taken from a population assumed to be normal, and = 1.2 and s = .6. Calculate a 98 percent confidence interval for μ.

A car insurance company would like to determine the proportion of accident claims covered by the company. According to a preliminary estimate, 60 percent of the claims are covered. How large a sample should be taken to estimate the proportion of accident claims covered by the company if we want to be 98 percent confident that the sample percentage is within ±3 percent of the actual percentage of the accidents covered by the insurance company?

Given the following test scores, find a 95 percent confidence interval for the population mean: 148, 154, 158, 160, 161, 162, 166, 170, 182, 195, 236. Assume population normality.

At the end of 1990, 1991, and 1992, the average prices of a share of stock in a portfolio were $34.83, $34.65, and $31.26 respectively. To investigate the average share price at the end of 1993, a random sample of 30 stocks was drawn and their closing prices on the last trading day of 1993 were observed with a mean of 33.583 and a standard deviation of 19.149. Estimate the average price of a share of stock in the portfolio at the end of 1993 with a 90 percent confidence interval.

The weight of a product is measured in pounds. A sample of 50 units is taken from a recent production. The sample yielded = 75 lb, and we know that σ² = 100 lb. Calculate a 95 percent confidence interval for μ.

When constructing a confidence interval, as the confidence level required in estimating the mean increases, the width of the confidence interval ________.

Researchers 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 93 percent confidence interval for the mean hours spent on personal tasks for 45- to 64-year-olds.