Describe the changes to the regression coefficient of Gender and its statistical

Question

Describe the changes to the regression coefficient of Gender and its statistical significance when Degree Type is added to the model in Step 2. Considering also the result in Question 2 in Task 1, discuss if there is any gender difference in test performance.

This is the answer to Task 1 question 2 :

In order to investigate gender difference in test performance you conduct separate two-sample t-tests. (Conduct your tests at a = 5 %.)

(a)      Considering the whole sample of 694 students, test if there is a difference in the average test performance between female and male students.

  

Level of significance, a = 5%

Test statistic: T

Decision Rule

Reject Ho, if p-value < 5%

Calculate the p-value

= (29.705 – 27.781) = 1.924

= P (tdf=690 >2.0613) = 0.0395776 (from excel)

Since p-value is less than 5%, therefore, there is sufficient evidence to reject the null hypothesis, so therefore, there is evidence in difference in the average test performance between female and male students.

SUMMARY OUTPUT Regression Statistics Multiple R 0.19476248 R Square 0.03793242 Adjusted R Square 0.03514786 Standard Error 12.0994024 Observations 694 ANOVA df SS MS F Significance F Regression 2 3988.51197 1994.25599 13.6223823 1.5759E-06 Residual 691 101159.316 146.395538 Total 693 105147.828 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 32.5498036 0.87611046 37.1526251 7.019E-167 30.8296457 34.2699615 30.8296457 34.2699615 Gender (M=1) -1.45054741 0.92408686 -1.56970895 0.11694061 -3.26490232 0.3638075 -3.26490232 0.3638075 Degree type (Single=1) -4.6621781 0.97513589 -4.78105475 2.1319E-06 -6.57676284 -2.74759336 -6.57676284 -2.74759336

Explanation / Answer

r^2 ajusted increases with additional of significant variables.

with F = 13.6 and p-value < 0.05 i can say that model is significant

ho: gender is not significant. v/s h1: gender is significant. with t = -1.5 and p-value > 0.05 i fail to reject ho and conclude that gender is not significat. that is there is no signifcant difference in the mean test performance between males and females. hence result is different in tak1 q2

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