Exam 9: Statistical Inference and Sampling Distributions

A population that consists of 250 items has a mean of 37 and a standard deviation of 13. A sample of size 5 is taken at random from this population. The standard error of the sample mean equals (up to three decimal places):

The standard deviation of the sampling distribution of the sample mean is also called the:

An auditor knows from past history that the average accounts receivable for a company is $521.72, with a standard deviation of $584.64. If the auditor takes a simple random sample of 100 accounts, what is the probability that the mean of the sample will be within $120 of the population mean?

Consider an infinite population with a mean of 100 and a standard deviation of 20. A random sample of size 50 is taken from this population. The standard deviation of the sample mean equals 3.2.

The standard deviation of a sampled population is also called the standard error of the sample mean.

The sampling distribution of the sample proportion is always normally distributed.

As a general rule in computing the standard error of the sample mean, the finite population correction factor is used only if the:

A sample of 30 observations is drawn from a normal population with mean of 750 and a standard deviation of 300. Suppose the population size is 600. a. Find the expected value of the sample mean $\bar { X }$ . b. Find the standard error of the sample mean $\bar { X }$ . c. Find P( $\bar { X }$ > 790). d. Find P( $\bar { X }$ < 650). e. Find P(760 < $\bar { X }$ < 810).

The standard error of the mean is the standard deviation of the sampling distribution of $\bar { X }$ .