Exam 8: Estimating Single Population Parameters

Suppose an airline decides to conduct a survey of its customers to determine their opinion of a proposed one-bag limit. The plan calls for a random sample of customers on different flights to be given a short written survey to complete during the flight. One key question on the survey will be: "Do you approve of limiting the number of carry-on bags to a maximum of one bag?" Airline managers expect that only about 15% will say "yes." Based on this assumption, what size sample should the airline take if it wants to develop a 95% confidence interval estimate for the population proportion who will say "yes" with a margin of error of ±0.02?

A Parks and Recreation official surveyed 200 people at random who have used one of the city's parks. The survey revealed that 26 resided outside the city limits. If she had to arrive at one single value to estimate the true proportion of park users who are residents of the city it would be 0.13.

Suppose a study estimated the population mean for a variable of interest using a 99% confidence interval. If the width of the estimated confidence interval (the difference between the upper limit and the lower limit) is 600 and the sample size used in estimating the mean is 1,000, what is the population standard deviation?

A 95 percent confidence interval for a mean can be interpreted that we are 95 percent sure that our answer is correct.

A sample of 250 people resulted in a confidence interval estimate for the proportion of people who believe that the federal government's proposed tax increase is justified is between 0.14 and 0.20. Based on this information, what was the confidence level used in this estimation?

Suppose a study of 196 randomly sampled privately insured adults with incomes over 200% of the current poverty level is to be used to measure out-of-pocket medical expenses for prescription drugs for this income class. The sample data are in the file Drug Expenses. Based on the sample data, construct a 95% confidence interval estimate for the mean annual out-of-pocket expenditures on prescription drugs for this income class. Interpret this interval.

When using a 95 percent confidence interval for a mean, the area in the upper tail of the distribution that is outside the interval is 5 percent.

The impact on the margin of error for a confidence interval for an increase in confidence level and a decrease in sample size is unknown since these changes are contradictory.

To find a 98 percent confidence interval where the standard deviation is known, the correct z-value to use for the critical value is 2.33.

When estimating sample size, a 90 percent confidence level will result in a smaller sample size than a 95 percent confidence level.

The file Danish Coffee contains a random sample of 144 Danish coffee drinkers and measures the annual coffee consumption in kilograms for each sampled coffee drinker. A marketing research firm wants to use this information to develop an advertising campaign to increase Danish coffee consumption. Based on the sample's results, what is the best point estimate of average annual coffee consumption for Danish coffee drinkers?

A production process that fills 12-ounce cereal boxes is known to have a population standard deviation of 0.009 ounce. If a consumer protection agency would like to estimate the mean fill, in ounces, for 12-ounce cereal boxes with a confidence level of 92% and a margin of error of 0.001, what size sample must be used?

A pilot sample of 75 items was taken, and the number of items with the attribute of interest was found to be 15. How many more items must be sampled to construct a 99% confidence interval estimate for p with a 0.025 margin of error?

Which of the following statements applies to a point estimate?

The general format for a confidence interval is:

In estimating a population mean, increasing the confidence level will result in a higher margin of error for a given sample size.

In an application to estimate the mean number of miles that downtown employees commute to work roundtrip each day, the following information is given: n = 20 = 4.33 s = 3.50 Based on this information, the upper limit for a 95 percent confidence interval estimate for the true population mean is:

The U.S. Post Office is interested in estimating the mean weight of packages shipped using the overnight service. They plan to sample 300 packages. A pilot sample taken last year showed that the standard deviation in weight was about 0.15 pound. If they are interested in an estimate that has 95 percent confidence, what margin of error can they expect?

The manager in charge of concessions at an NFL football stadium is interested in estimating the mean dollars that are spent per person attending the games. A pilot sample of n = 50 people has revealed a sample mean and standard deviation of $12.35 and $2.35 respectively. He wishes to estimate the population mean within ± $0.20 of the true mean and wishes to have a confidence level of 95 percent. Given this, he needs to sample an additional 481 people.

A major tire manufacturer wishes to estimate the mean tread life in miles for one of its tires. It wishes to develop a confidence interval estimate that would have a maximum sampling error of 500 miles with 90 percent confidence. A pilot sample of n = 50 tires showed a sample standard deviation equal to 4,000 miles. Based on this information, the required sample size is: