Exam 8: Estimating Single Population Parameters

If a pilot sample of n = 40 items has been used as a first step in determining a required sample size of n = 360, the decision maker can go ahead and use these 40 and take a sample of only 320 more items.

A grocery store manager is interested in estimating the mean weight of apples received in a shipment. If she wishes to have the estimate be within ±.05 pound with 90 percent confidence, the sample size should be 103 apples if she believes that the standard deviation is .08 pound.

In a situation where the population standard deviation is known and we wish to estimate the population mean with 90 percent confidence, what is the appropriate critical value to use?

Which of the following statements is true with respect to the t-distribution?

A random sample of 121 automobiles traveling on an interstate showed an average speed of 65 mph. From past information, it is known that the standard deviation of the population is 22 mph. The 95 percent confidence interval for μ is determined as (61.08, 68.92). If we are to reduce the sample size to 100 (other factors remain unchanged), the 95 percent confidence interval for μ would:

A toy store wants to estimate the mean number of purchases online daily. The standard deviation is known. If they want to find a 99 percent confidence interval the critical value to use is:

Most major airlines allow passengers to carry two pieces of luggage (of a certain maximum size) onto the plane. However, their studies show that the more carry-on baggage passengers have, the longer it takes to unload and load passengers. One regional airline is considering changing its policy to allow only one carry-on per passenger. Before doing so, it decided to collect some data. Specifically, a random sample of 1,000 passengers was selected. The passengers were observed, and the number of bags carried on the plane was noted. Out of the 1,000 passengers, 345 had more than one bag. Suppose the airline also noted whether the passenger was male or female. Out of the 1,000 passengers observed, 690 were males. Of this group, 280 had more than one bag. Using this data, obtain and interpret a 95% confidence interval estimate for the proportion of male passengers in the population who would have been affected by the one-bag limit.

Compute the 90% confidence interval estimate for the population proportion, p, based on a sample size of 100 when the sample proportion, is equal to 0.40.

A random sample of n = 500 people was surveyed recently to determine an estimate for the proportion of people in the population who had attended at least some college. The estimate concluded that between 0.357 and 0.443 of the population had attended. Given this information, we can determine that the confidence level was approximately 95 percent.

When developing a confidence interval estimate, the confidence level is calculated based on the size of the sample and the population standard deviation.

When a decision maker determines the required sample size for estimating a population mean, a change in the confidence level will result in a change in the required sample size, provided that the margin of error is also modified accordingly.

A point estimate for a population mean lies exactly halfway between the outer and lower limits of its confidence interval estimate.

When σ is unknown, one should use an estimate that is considered to be at least as large as the true σ. This will provide a conservative sample size to be on the safe side.

The makers of weight loss product are interested in estimating the mean weight loss for users of their product. To do this, they have selected a random sample of n = 9 people and have provided them with a supply of the product. After six months, the nine people had an average weight loss of 15.3 pounds with a standard deviation equal to 3.5 pounds. The upper limit for the 90 percent confidence interval estimate for the population mean is approximately 17.47 pounds.

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. Develop and interpret a 90% confidence interval estimate for the mean annual coffee consumption of Danish coffee drinkers.

The standard deviation for the checking account balances is assumed known to be $357.50. Recently, a bank manager was interested in estimating the mean balance. To do this, she selected a random sample of 81 accounts and found a mean balance of $1,347.20. At a 95 percent confidence level, the lower limit for the confidence interval is $646.50.

The main purpose of a pilot sample in an application involving an estimate for a population mean is to determine what the margin of error will likely be.

In order to reduce the cost of a study, a marketing manager wants to reduce the sample size for a study of customer response to a recent advertising campaign. What can she do that would lead to a reduction in sample size?

All of the factors that are needed to determine the required sample size are within the control of the decision maker.

A random sample of 340 people in Chicago showed that 66 listened to WJKT-1450, a radio station in South Chicago Heights. Based on this sample information, what is the point estimate for the proportion of people in Chicago that listen to WJKT-1450?