Exam 7: Introduction to Sampling Distributions

Suppose a population is normally distributed with a mean 100 and a standard deviation of 15.When a sample of size n = 36 is collected a sampling distribution is created.Explain which is larger: the probability of a value randomly selected from the population being larger than 120,or the probability of a sample mean being larger then 120.

The sample mean is a parameter.

The proportion of parts in an inventory that are outdated and no longer useful is thought to be 0.10.To check this,a random sample of n = 100 parts is selected and 14 are found to be outdated.Based upon this information,what is the probability of 14 or more outdated parts?

A sampling distribution for is the distribution of all possible sample means that could be computed from the possible samples of a given sample size.

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?

In order to assume that the sampling distribution for a proportion is approximately normal,the population proportion must be very close to 0.50.

A major shipping company has stated that 96 percent of all parcels are delivered on time.To check this,a random sample of n = 200 parcels were sampled.Of these,184 arrived on time.If the company's claim is correct,what is the probability of 184 or fewer parcels arriving on time?

In a recent report,it was stated that the proportion of employees who carpool to their work is 0.14 and that the standard deviation of the sampling proportion is 0.0259.However,the report did not indicate what the sample size was.What was the sample size?

Sampling error is the difference between the population value and the sample statistic.

The State Department of Weights and Measures is responsible for making sure that commercial weighing and measuring devices,such as scales,are accurate so customers and businesses are not cheated.Periodically,employees of the department go to businesses and test their scales.For example,a dairy bottles milk in 1-gallon containers.Suppose that if the filling process is working correctly,the mean volume of all gallon containers is 1.00 gallon with a standard deviation equal to 0.10 gallons.Based on this information,if the department employee selects a random sample of n = 9 containers,what is the probability that the mean volume for the sample will be greater than 1.01 gallons?

A company has determined that the mean number of days it takes to collect on its accounts receivable is 36 with a standard deviation of 11 days.The company plans to select a random sample of n = 12 accounts and compute the sample mean.Which of the following statements holds true in this situation?

The annual income for independent sales representatives in the United States is thought to be highly right-skewed with a mean equal to $144,300 and a standard deviation of $32,450.Given this information,if a sample of 36 independent sales representatives is selected,what is the probability that the mean of the sample will exceed $130,000?

The St.Joe Company grows pine trees and the average annual increase in tree diameter is 3.1 inches with a standard deviation of 0.5 inches.A random sample of n = 50 trees is collected.What is the probability of the sample mean being less the 2.9 inches?

When a population is not normally distributed,the Central Limit Theorem states that a sufficiently large sample will result in the sample mean being normally distributed.

If it is desired that sampling error be reduced,one step that tends to work is to increase the sample size that is selected from the population.

One of the things that the Central Limit Theorem tells us is that about half of the sample means will be greater than the population mean and about half will be less.

The sampling distribution for is actually the distribution of possible sampling error for samples of a given size selected at random from the population.

If the mean age for all students that attend your university is 24.78 years,it would be reasonable to expect that the mean of a sample of students selected from that population would also equal 24.78 years as long at the sampling is done using sound statistical methods.

Sampling error occurs when the population parameter and the sample statistic are different.

The mean of a sampling distribution would be equal to the mean of the population from which the sampling distribution is constructed.