# Sampling distribution of the sample mean is approx normal

1.Which of the following statements about the sampling distribution of the sample mean is incorrect?

a. The sampling distribution of the sample mean is approximately normal whenever the sample size is sufficiently large (n>30).

b. The sampling distribution of the sample mean is generated by repeatedly taking samples of size n and computing the sample means.

c. The mean of the sampling distribution of the sample mean is equal to µ (population mean)

d. The standard deviation of the sampling distribution of the sample mean is equal to (sigma) population standard deviation;.

2. The standard error of the proportion will become larger as:

a. p approaches 0

b. p approaches 0.5

c. p approaches 1.00

d. n increases

3. The t distribution

a. assumes the population is normally distributed.

b. approaches the normal distribution as the sample size increases.

c. has more area in the tails than does the normal distribution.

d. All of the above.

4. Assume a 95% confidence interval for µ turns out to be (1000, 2100). To make more useful inferences from the data, the researcher wants to reduce the width of the confidence interval. Which of the following will result in a reduced confidence interval width?

a. Increase the sample size.

b. Decrease the confidence level.

c. Increase the sample size and decrease the confidence level.

d. Increase the confidence level and decrease the sample size.

5. In the construction of confidence intervals, if all other quantities are unchanged, an increase in the sample size will lead to a ___________ interval.

a. narrower

b. wider

c. less significant

d. biased

#### Solution Preview

1.d. The standard deviation of the sampling distribution of the sample mean is standard deviation divided by root of sample size.

2. b. p approaches ...

#### Solution Summary

This post answer five conceptual questions on sampling, hypothesis testing and confidence interval