Exam 7: Introduction to Sampling Distributions

Given a population in which the probability of success is p =0.20, if a sample of 500 items is taken, then calculate the probability the proportion of successes in the sample will be between 0.18 and 0.23.

The population mean of income for adults in a particular community is known to be $28,600. Given this information, the sampling distribution of values will be less than this depending on the size of the sample used in developing the sampling distribution.

A major textbook publisher has a contract with a printing company. Part of the contract stipulates that no more than 5 percent of the pages should have any type of printing error. As a quality control measure, the publisher periodically selects a random sample of n = 100 pages. Then, depending on the proportion of pages with errors, they either say nothing to the printer or they complain that the quality has slipped. Suppose the publisher wants no more than a .10 chance of mistakenly blaming the printer for poor quality, what should the cut-off proportion be?

In an article entitled "Fuel Economy Calculations to Be Altered," James R. Healey indicated that the government planned to change how it calculates fuel economy for new cars and trucks. This is the first modification since 1985. It is expected to lower average mileage for city driving in conventional cars from 10% to 20%. AAA has forecast that the 2008 Ford F-150 would achieve 15.7 mile per gallon (mpg). The 2008 Ford F-150 was tested by AAA members driving the vehicle themselves and was found to have an average of 14.3 mpg. Assume that the mean obtained by AAA members is the true mean for the population of 2008 Ford F-150 trucks and that the population standard deviation is 5 mpg. Suppose 100 AAA members were to test the 2008 F-150. Determine the probability that the average mpg would be at least 15.7.

According to an industry report, 26 percent of all households have at least one cell phone. Further, of those that do have a cell phone, the mean monthly bill is $55.90 with a standard deviation equal to $9.60. Recently, a random sample of 400 households was selected. Of these households, 88 indicated that they had cell phones. The mean bill for these 88 households was $57.00. What is the probability of getting 88 or fewer households with cell phones if the numbers provided by the industry report are correct?

The size of the sampling error that comes from a random sample depends on both the variation in the population and the size of the sample being selected.

A particular subdivision has 20 homes. The number of people living in each of these homes is listed as follows: If a random sample of n = 3 homes were selected, what would be the highest possible positive sampling error?

When sampling from a population, the sample mean will:

The following values represent the population of home mortgage interest rates (in percents) being charged by the banks in a particular city: Given this information, what is the most extreme amount of sampling error possible if a random sample of n = 3 banks is surveyed and the mean loan rate is calculated?

The sample mean is a parameter.

Indicate why the Central Limit Theorem is so important in the application of statistical analysis.

Assume that n = 18 people are asked a yes/no survey question, and 6 people say "yes" while 12 people say "no." Based on this information the sample proportion can be assumed normally distributed.

In analyzing the sampling distribution of a proportion, doubling the sample size will cut the standard deviation of the sampling distribution in half.

According to the most recent Labor Department data, 10.5% of engineers (electrical, mechanical, civil, and industrial) were women. Suppose a random sample of 50 engineers is selected. How likely is it that the random sample of 50 engineers will contain 8 or more women in these positions?

If a population is not normally distributed, then the sampling distribution for the mean also cannot be normally distributed.

The proportion of parts in an inventory that are outdated and no longer useful is thought to be 0.10. To check this, a random sample of n = 100 parts is selected and 14 are found to be outdated. Based upon this information, what is the probability of 14 or more outdated parts?

In a campaign speech, a candidate for governor stated that about 63 percent of the people in the state were in favor of spending additional money on higher education. After the speech, a polling agency surveyed a random sample of 400 people and found 234 people who favored more spending on higher education. Based on the candidate's statement, the probability of finding 234 or fewer is approximately 0.97.

Suppose the mean balance of checking accounts at Regions Bank is known to be $4320. A random sample of 10 accounts yields a total of $41,490. This means the sampling error is -$171.

A pharmaceutical company claims that only 5 percent of patients experience nausea when they take a particular drug. In a research study, n = 100 patients were given this drug and 8 experienced nausea. Assuming that the company's claim is true, what is the probability of 8 or more patients experiencing nausea?

If the standard error for the sampling distribution of a proportion is equal to 0.0327 and if the population proportion, p, is equal to .80, the sample size must be 150.