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150 Chapter 3 Review of Statistics

CPS92_12_Description, available on the website. Use these data to answer
the following questions.

a. i. Compute the sample mean for average hourly earnings (AHE) in
1992 and 2012.

ii. Compute the sample standard deviation for AHE in 1992 and
2012.

iii. Construct a 95% confidence interval for the population means of
AHE in 1992 and 2012.

iv. Construct a 95% confidence interval for the change in the popula-
tion mean of AHE between 1992 and 2012.

b. In 2012, the value of the Consumer Price Index (CPI) was 229.6. In
1992, the value of the CPI was 140.3. Repeat (a) but use AHE mea-
sured in real 2012 dollars ($2012); that is, adjust the 1992 data for the
price inflation that occurred between 1992 and 2012.

c. If you were interested in the change in workers’ purchasing power
from 1992 to 2012, would you use the results from (a) or (b)? Explain.

d. Using the data for 2012:

i. Construct a 95% confidence interval for the mean of AHE for
high school graduates.

ii. Construct a 95% confidence interval for the mean of AHE for
workers with a college degree.

iii. Construct a 95% confidence interval for the difference between
the two means.

e. Repeat (d) using the 1992 data expressed in $2012.

f. Using appropriate estimates, confidence intervals, and test statistics,
answer the following questions:

i. Did real (inflation-adjusted) wages of high school graduates
increase from 1992 to 2012?

ii. Did real wages of college graduates increase?

iii. Did the gap between earnings of college and high school gradu-
ates increase? Explain.

g. Table 3.1 presents information on the gender gap for college gradu-
ates. Prepare a similar table for high school graduates, using the 1992
and 2012 data. Are there any notable differences between the results
for high school and college graduates?