Exam 8: Sampling Methods and the Central Limit Theorem

Sampling error is defined as ________.

The Office of Student Services at a large western state university maintains information on the study habits of its full-time students. Their studies indicate that the mean amount of time undergraduate students study per week is 20 hours. The hours studied follows the normal distribution with a population standard deviation of six hours. Suppose we select a random sample of 144 current students. What is the standard error of the mean?

The tread life of tires mounted on light-duty trucks follows the normal probability distribution with a population mean of 60,000 miles and a population standard deviation of 4,000 miles. Suppose you bought a set of four tires,what is the likelihood the mean tire life of these four tires is between 57,000 and 63,000 miles?

Bones Brothers & Associates prepare individual tax returns. Over prior years,Bones Brothers has maintained careful records regarding the time to prepare a return. The mean time to prepare a return is 90 minutes and the population standard deviation of this distribution is 14 minutes. Suppose 100 returns from this year are selected and analyzed regarding the preparation time. What assumptions do you need to make about the shape of the population distribution of all possible tax preparation times to make inferences about the mean time to complete a tax form?

We can expect some difference between sample statistics and the corresponding population parameters. This difference is called the sampling error.

The mean of all possible sample means is equal to ________.

Mileage tests were conducted on a randomly selected sample of 100 newly developed automobile tires. The sample mean tread wear was 50,000 miles,with a population standard deviation of 3,500 miles. What is the best estimate of the average tread life in miles for the entire population of these tires?

Bones Brothers & Associates prepare individual tax returns. Over prior years,Bones Brothers has maintained careful records regarding the time to prepare a return. The mean time to prepare a return is 90 minutes,and the population standard deviation of this distribution is 14 minutes. Suppose 100 returns from this year are selected and analyzed regarding the preparation time. What is the standard error of the mean?

The wildlife department has been feeding a special food to rainbow trout fingerlings in a pond. Based on a large number of observations,the distribution of trout weights is normally distributed with a mean of 402.7 grams and a standard deviation of 8.8 grams. What is the probability that the mean weight for a sample of 40 trout exceeds 405.5 grams?

An experiment involves selecting a random sample of 256 middle managers for study. One item of interest is their annual income. The sample mean is computed to be $35,420. If the population standard deviation is $2,050,what is the standard error of the mean?

The true sampling error is usually not known because ________.

The weight of trucks traveling on a particular section of I-475 has a population mean of 15.8 tons and a population standard deviation of 4.2 tons. What is the probability a state highway inspector could select a sample of 49 trucks and find the sample mean to be 14.3 tons or less?

The Intelligence Quotient (IQ)test scores for adults are normally distributed with a population mean of 100 and a population standard deviation of 15. What is the probability we could select a sample of 50 adults and find the mean of this sample is less than 95?

It is often not feasible to study the entire population because it is impossible to observe all the items in the population.

For a population that is not normally distributed,the distribution of the sample means will ________.

Bones Brothers & Associates prepare individual tax returns. Over prior years,Bones Brothers has maintained careful records regarding the time to prepare a return. The mean time to prepare a return is 90 minutes,and the population standard deviation of this distribution is 14 minutes. Suppose 100 returns from this year are selected and analyzed regarding the preparation time. What is the probability that the mean time for the sample of 100 returns is between 88 minutes and 92 minutes?

A marketing firm is studying consumer preferences for winter fashions in four different months. From a population of women 18 to 21 years of age,a random sample of 100 women was selected in January. Another random sample of 100 women was selected in March. Another random sample of 100 women was selected in June. Another random sample of 100 women was selected in September. What is the number of samples?

A sampling distribution of the means is a probability distribution consisting of all possible sample means of a given sample size selected from a population.

How many different samples of size 4 can be selected from a population of size 8?

When deciding to collect sample information rather than collecting information from the population,the amount of time required to collect the information is unimportant.