Salaries of technology professionals
The data in the table, obtained from Business Weeks technology section, represents typical salaries of technology professionals in 13 metropolitan areas for 2003 and 2005. Suppose you want to determine if the mean salary of technology professionals at all U.S. metropolitan areas has increased between 2003 and 2005.
TECHPRO
. . . . . . . . . . . . . .2003 Salary. . . . . . 2005 Salary
Metro Area. . . . . .($ thousands). . . . .($ thousands)
Silicon Valley. . . . .87.7. . . . . . . . . . .85.9
New York . . . . . . .78.6. . . . . . . . . . . 80.3
Washington, D.C. . 71.4. . . . . . . . . . .77.4
Los Angeles. . . . . .70.8. . . . . . . . . . .77.1
Denver. . . . . . . . . .73.0. . . . . . . . . . .77.1
Boston. . . . . . . . . .76.3. . . . . . . . . . .80.1
Atlanta. . . . . . . . . . 73.6. . . . . . . . . 73.2
Chicago. . . . . . . . . .71.1. . . . . . . . . .73.0
Philadelphia. . . . . . .69.5. . . . . . . . . .69.8
San Diego. . . . . . . .69.0. . . . . . . . . .77.1
Seattle. . . . . . . . . . 71.0. . . . . . . . . .66.9
Dallas-Ft. Worth. . . .73.0. . . . . . . . . 71.0
Detroit. . . . . . . . . . .62.3. . . . . . . . . .64.1
a. Set up the null and alternative hypothesis for the test.
b. Calculate the difference between the 2003 and 2005 salaries for each metropolitan area.
c. Find the mean and standard deviation of the differences, part b.
d. Use the results, part c, to calculate the test statistic.
e. Find the rejection region for the test at ? = 0.10.
f. Make the appropriate conclusion.
g. What conditions are required for the inference in part f to be valid? Are these conditions reasonably satisfied?
5 stars for best answer. Thanks.
The data in the table, obtained from Business Weeks technology section, represents typical salaries of technology professionals in 13 metropolitan areas for 2003 and 2005. Suppose you want to determine if the mean salary of technology professionals at all U.S. metropolitan areas has increased between 2003 and 2005.
TECHPRO
. . . . . . . . . . . . . .2003 Salary. . . . . . 2005 Salary
Metro Area. . . . . .($ thousands). . . . .($ thousands)
Silicon Valley. . . . .87.7. . . . . . . . . . .85.9
New York . . . . . . .78.6. . . . . . . . . . . 80.3
Washington, D.C. . 71.4. . . . . . . . . . .77.4
Los Angeles. . . . . .70.8. . . . . . . . . . .77.1
Denver. . . . . . . . . .73.0. . . . . . . . . . .77.1
Boston. . . . . . . . . .76.3. . . . . . . . . . .80.1
Atlanta. . . . . . . . . . 73.6. . . . . . . . . 73.2
Chicago. . . . . . . . . .71.1. . . . . . . . . .73.0
Philadelphia. . . . . . .69.5. . . . . . . . . .69.8
San Diego. . . . . . . .69.0. . . . . . . . . .77.1
Seattle. . . . . . . . . . 71.0. . . . . . . . . .66.9
Dallas-Ft. Worth. . . .73.0. . . . . . . . . 71.0
Detroit. . . . . . . . . . .62.3. . . . . . . . . .64.1
a. Set up the null and alternative hypothesis for the test.
b. Calculate the difference between the 2003 and 2005 salaries for each metropolitan area.
c. Find the mean and standard deviation of the differences, part b.
d. Use the results, part c, to calculate the test statistic.
e. Find the rejection region for the test at ? = 0.10.
f. Make the appropriate conclusion.
g. What conditions are required for the inference in part f to be valid? Are these conditions reasonably satisfied?
5 stars for best answer. Thanks.
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For small n's, use paired t-test, assume normality.
H0: µd = 0 (Equal, you may object, depends on your stat level of knowledge)
HA: µd > 0
Calculate the difference for each area, 2005 minus 2003.. Find its mean d-bar.
Calculate the variance for the differences, sd^2.
Standard deviation of the differences=sd.
t-value, t=(d-bar - 0) / [sd/sqrt(n)]
Get P{T>t} from table. Reject H0 if prob > 0.10, else do not reject.
Conclusion: If significant, has increased, otherwise data unanle to indicate so.
If you want fast numerical solution, use Excel package, paired t-test, very easy.
H0: µd = 0 (Equal, you may object, depends on your stat level of knowledge)
HA: µd > 0
Calculate the difference for each area, 2005 minus 2003.. Find its mean d-bar.
Calculate the variance for the differences, sd^2.
Standard deviation of the differences=sd.
t-value, t=(d-bar - 0) / [sd/sqrt(n)]
Get P{T>t} from table. Reject H0 if prob > 0.10, else do not reject.
Conclusion: If significant, has increased, otherwise data unanle to indicate so.
If you want fast numerical solution, use Excel package, paired t-test, very easy.