3. In a 95% confidence interval for a population proportion,

a. the margin of error is always less than the standard error of the proportion.

b. the margin of error can be less than, equal to, or greater than the standard error of the proportion.

c. the margin of error is always greater than the standard error of the proportion.

d. the margin of error is 2.33 times greater than the standard error of the proportion.

Four economists have made economic forecasts for next year. Three forecast a downturn, one forecast an upturn.

Economist W X Y Z

Forecast Down Up Down Down

Suppose you produce the 4 possible samples of size 3 that could be selected from this population of economists, determine the proportion of economists in each sample forecast a downturn, and produce the sampling distribution of this sample proportion. The mean (expected value) for this sampling distribution is

a. .50

b. .75

c. .675

d. .325

e. .25