Question

He Economic Policy Institute periodically issues reports on wages of entry-level workers. The institute reported that entry-level wages for male college graduates were $21.68 per hour and for female college graduates were $18.80 per hour in 2011 . Assume that the standard deviation for male graduates is $2.30, and for female graduates it is $2.05. (a) What is the sampling distribution of x

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for a random sample of 50 male college graduates? If required, round your answer to four decimal places. (b) What is the sampling distribution of x
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for a random sample of 50 female college graduates? If required, round your answer to four decimal places. (3) (c) In which of the preceding two cases, part (a) or part (b), is the standard error of x
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smaller? Why? The input in the box below will not be graded, but may be reviewed and considered by your instructor.

Answer 1

The sampling distribution of x for a random sample of 50 male college graduates is calculated using the standard error. The same method is applied to calculate the sampling distribution of x for a random sample of 50 female college graduates. The standard error is smaller when the sample size is larger.

Step-by-step explanation:

(a) To find the sampling distribution of x for a random sample of 50 male college graduates, we need to calculate the standard error. The standard error is the standard deviation divided by the square root of the sample size. So, for male college graduates:

Standard Error = Standard Deviation / √Sample Size = $2.30 / √50

(b) Similarly, for female college graduates:

Standard Error = Standard Deviation / √Sample Size = $2.05 / √50

(c) In both cases, the standard error is the same because the sample size is the same. The standard error measures the variability of the sample mean, and it is influenced by the sample size. With a larger sample size, the standard error becomes smaller.