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The Economic Policy Institute periodically issues reports on wages of entry-level workers. The institute reported that...

The 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 (Economic Policy Institute website, March 30, 2012). Assume the standard deviation for male graduates is $2.30, and for female graduates it is $2.05. Assume all samples referenced below are simple random samples and large enough so that the central limit theorem applies but small enough that the infinite population formulas apply.

a. What is the probability that a sample of 50 male graduates will provide a sample mean within $.50 of the population mean, $21.68?

b. What is the probability that a sample of 50 female graduates will provide a sample mean within $.50 of the population mean, $18.80?

c. In which of the preceding two cases, part (a) or part (b), do we have a higher probability of obtaining a sample estimate within $.50 of the population mean? Why?

d. What is the probability that a sample of 120 female graduates will provide a sample mean more than $.30 below the population mean?

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orchestra answered 2 years ago
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