Exam 9: Sampling Distributions

Which of the following is true about the sampling distribution of the sample mean?

A sample of size 200 is taken at random from an infinite population. Given that the population proportion is 0.60, the probability that the sample proportion is greater than 0.58 is:

A sample of size 25 is selected from a population of size 500. The finite population correction is needed to find the standard error of $\bar { X }$ .

NARRBEGIN: Mean Salary Mean Salary In order to estimate the mean salary for a population of 500 employees, the president of a certain company selected at random a sample of 40 employees.NARREND -{Mean Salary Narrative} Would you use the finite population correction factor in calculating the standard error of the sample mean in this case? Explain.

A sample of size 40 is taken from an infinite population whose mean and standard deviation are 68 and 12, respectively. The probability that the sample mean is larger than 70 equals

The mean of the sampling distribution of the sample proportion $\tilde{ p }$ , when the sample size n = 100 and the population proportion p = 0.92, is 92.0.

The amount of bleach a machine pours into bottles has a mean of 50 ounces with a standard deviation of 0.25 ounces. We take a random sample of 36 bottles filled by this machine. The sampling distribution of the sample mean has a mean of 50 ounces.

NARRBEGIN: Magazines Magazines A local magazine store sells an average of 2,100 magazines per day, with a standard deviation of 500 magazines. Consider a sample of 60 days of operation.NARREND -{Magazines Narrative} What is the shape of the sampling distribution of the sample mean number of magazines sold per day? Why?

NARRBEGIN: Number of Fish Tanks Number of Fish Tanks The following data give the number of fish tanks owned for a population of 4 families. Family A B C D Number af Fish Tanks Owned 2 1 4 3 NARREND -{Number of Fish Tanks Narrative} Find the mean and the standard deviation for the population.

A CPA 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 is within $120 of the population mean?

If two random samples of sizes 30 and 36 are selected independently from two populations with means 78 and 85, and standard deviations 12 and 15, respectively, then the standard error of the difference $\bar { X } _ { 1 }$ and $\bar { X } _ { 2 }$ is equal to:

NARRBEGIN: Graduate Internships Graduate Internships The chairman of the Biology department in a certain college believes that 70% of the department's graduate internships are given to international students. A random sample of 50 graduate interns is taken.NARREND -{Graduate Internships Narrative} Find the expected value and the standard error of the sampling distribution of $\tilde{ p }$ .

The standard error of the difference between sample means, $\bar { X } _ { 1 } - \bar { X } _ { 2 }$ , is calculated by the formula $\sigma _ { \bar { x } _ { 1 } - \bar { x } _ { 2 } } = \sqrt { \sigma _ { 1 } ^ { 2 } / n _ { 1 } - \sigma _ { 2 } ^ { 2 } / n _ { 2 } }$ where $\sigma _ { i } ^ { 2 }$ is the variance of population i (i = 1, 2).

Which of the following statements about the sampling distribution of $\bar { X }$ is NOT true?

What is the probability that you get more than 200 heads if you flip a coin 400 times?

The standard deviation of $\tilde{ p }$ is also called the:

If all possible samples of size n are drawn from an infinite population with a mean of 15 and a standard deviation of 5, then the standard error of the sample mean equals 1.0 for samples of size:

As the size of the sample is increased, the mean of $\bar { X }$ increases.

Given that X is a binomial random variable with very large n, the binomial probability P(X $\le$ 5) is approximated by the area under a normal curve to the left of

A sample of 250 observations is selected at random from an infinite population. Given that the population proportion is .25, the standard error of the sampling distribution of the sample proportion is: