Stat-351 Chpt 8, 9e

For a sample size of 1, the sampling distribution of the mean is normally distributed:

only if the population is 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:

sample size is greater than 5% of the sample size.

If all possible samples of size n are drawn from a population, the probability distribution of the sample mean is called the:

sampling distribution of X.

The finite population correction factor should be used:

whenever the sample size is large compared to the population size.

Given a binomial distribution with n trials and probability p of a success on any trial, a conventional rule of thumb is that the normal distribution will provide an adequate approximation of the binomial distribution if:

np 5 and n(1-p) > or equal to 5

As a general rule, the normal distribution is used to approximate the sampling distribution of the sample proportion only if:

np and n(1-p) are both greater than or equal to 5.

If all possible samples of size n are drawn from an infinite population with a mean of u and a standard deviation of & , then the standard error of the sample mean is inversely proportional to:

Square root n

The expected value of the sampling distribution of the sample mean equals the population mean :

for all populations.

The Central Limit Theorem states that, if a random sample of size n is drawn from a population, then the sampling distribution of the sample mean :

is approximately normal if n > 30.

Given that X is a binomial random variable with very large n, the binomial probability P(X > or equal to 5) is approximated by the area under a normal curve to the right of:

4.5

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

standard error of the sample mean.

The standard deviation of P hat is also called the:

standard error of the sample proportion.

Which of the following is true regarding the sampling distribution of the mean for a large sample size? Assume the population distribution is not normal.

It has the same mean as the population, but a different shape and standard deviation.

A sample of size n is selected at random from an infinite population. As n increases, which of the following statements is true?

The standard error of the sample mean decreases.

The standard error of the sample proportion gets larger as:

p approaches 0.50