6. Evaluate the following statement using data from the NLSW88. To access the data, type, sysuse nlsw88 into Stata.

Union employees earn significantly higher wages and work significantly fewer hours than non-union employees.

This is widely believed about unionized employeesthey earn more for doing less.Implied here is an association between union membership (the EV) and both hourly wages and hours worked per week (the RVs)

Complete the following steps to evaluate this claim.

a) State the null hypotheses and alternative hypotheses associated with this claim.

Null: There is no difference between both hourly wages and/or hours worked per week for union and non-union members.

Alternative: There is an association between hourly wages and hours worked per week according to whether a person is or is not a union member.

b) Identify the statistical tests (one for each EV/RV combination) that will allow you to test these hypotheses.Explain why you believe each statistical test is the appropriate choice.

c) Locate the variables in the NLSW88 data file that represent the EV (UNION) and the RVs (WAGE, HOURS).Run you chosen statistical tests using Stata, and paste the output for each statistical test below.

union | Summary of hourly wage

worker |Mean Std. Dev. Freq.

------------+------------------------------------

nonunion | 7.2046688 4.1036938 1,417

union | 8.6742941 4.1745389 461

------------+------------------------------------

Total | 7.5654235 4.1683693 1,878

Analysis of Variance

SourceSS dfMSF Prob > F

------------------------------------------------------------------------

Between groups751.2568031 751.256803 44.23 0.0000

Within groups31862.1856 1876 16.9841074

------------------------------------------------------------------------

Total 32613.4424 1877 17.3753023

Bartlett's test for equal variances:chi2(1) = 0.2045Prob>chi2 = 0.651

union |Summary of usual hours worked

worker |Mean Std. Dev. Freq.

------------+------------------------------------

nonunion | 37.262006 10.227234 1,416

union | 38.659436 9.1101391 461

------------+------------------------------------

Total | 37.605221 9.9802702 1,877

Analysis of Variance

SourceSS dfMSF Prob > F

------------------------------------------------------------------------

Between groups679.1414761 679.1414766.84 0.0090

Within groups186181.327 1875 99.2967079

------------------------------------------------------------------------

Total 186860.469 1876 99.6057936

Bartlett's test for equal variances:chi2(1) = 8.9135Prob>chi2 = 0.003

d) Interpret the results, and determine which portions of the statement above (if any) are supported by the evidence and which (if any) are not. Support all claims by reporting the appropriate descriptive statistics and the test statistics/p-values that tell whether the differences in the values of the descriptive statistics are significant.