Question

Suppose the following table was generated from sample data of 20 20 employees relating hourly wage to years of experience and whether or not they have a college degree. Using statistical software, create an indicator (dummy) variable for the variable "Degree" and find the regression equation. Is there enough evidence to support the claim that on average employees with a college degree have higher hourly wages than those without a college degree at the 0.05 0.05 level of significance? If yes, write the coefficient of the dummy variable in the space provided, rounded to two decimal places. Else, select "There is not enough evidence." Copy Data Hourly wages of employees Wage Experience Degree 15.06 15.06 12 12 No 21.00 21.00 16 16 Yes 22.05 22.05 17 17 Yes 17.19 17.19 20 20 No 15.51 15.51 14 14 No 18.65 18.65 23 23 No 28.44 28.44 28 28 Yes 1.95 1.95 1 1 Yes 13.58 13.58 9 9 Yes 13.60 13.60 8 8 No 13.43 13.43 9 9 No 32.16 32.16 28 28 Yes 19.55 19.55 27 27 No 17.04 17.04 19 19 No 22.39 22.39 17 17 Yes 16.85 16.85 19 19 No 15.66 15.66 10 10 Yes 18.30 18.30 13 13 Yes 16.00 16.00 16 16 No 22.21 22.21 17 17 Yes

Answer 1

There is enough evidence to support the claim that on average employees with a college degree have higher hourly wages than those without a college degree at the 0.05 level of significance

following regression analysis information has been generated using ms-excel. here wage is used as dependent or response variable and experience and degree as independent variable or predictor .

here degree is transformed into coded variable Yes=1, No=0

since the p-value=0.0026 of the independent variable Degree is less than typical significance level alpha=0.05, (and also it is positive 4.3137 ) so there is significant difference between the level of degree (yes or no ) and conclude that there is enough evidence to support the claim that on average employees with a college degree have higher hourly wages than those without a college degree at the 0.05 level of significance

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.908152055
R Square	0.824740155
Adjusted R Square	0.80412135
Standard Error	2.723334927
Observations	20
ANOVA
	df	SS	MS	F	Significance F
Regression	2	593.3155769	296.6578	39.99942	3.7265E-07
Residual	17	126.0814031	7.416553
Total	19	719.39698
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	3.721360978	1.714909235	2.170005	0.044467	0.103218792	7.339503165
experience	0.752493355	0.088801777	8.473855	1.65E-07	0.565137984	0.939848725
degree	4.31374269	1.221823387	3.530578	0.002568	1.735920699	6.891564682