Question

The following results are from data concerning the amount withdrawn from an ATM machine based on the amount of time spent at the ATM machine (SECONDS) and the gender, FEMALE (dummy variable = 1 for females and = 0 for males) and an interaction term, SECONDS*FEMALE

  

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.503
R Square
Adjusted R Square
Standard Error
Observations	50
ANOVA
	df	SS	MS	F	Significance F
Regression			2728.7	5.19	0.004
Residual		24161.8	525.3
Total		32348
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	133.5	23.51	5.89	0	91.03	185.67
Seconds	-2	0.679		0.002	-3.401	-0.839
Female	-78.6	30.3	-2.26		-137.33	-8.07
Seconds*Female	2.3	0.85	2.8	0.007	0.67

  
Based on the regression results, when testing to see if the coefficient on FEMALE is different than -100, what is the critical value (using the 5% level of significance)? (please express your answer using 2 decimal places)

Answer 1

Let be the coefficient on Female. Then the hypotheses are

Null Hypotheis H0: = -100

Alternative Hypothesis H1: -100

Test statistic, t = (Observed Coeff - Hypothesized Coeff) / Standard error

= (-78.6 - (-100)) / 30.3

= 0.7063

Degree of freedom = Number of Observations - Number of predictors - 1

= 50 - 3 - 1

= 46

For two tail test, Critical value of t at 5% level of significance and df = 46 is 2.01

We reject H0 when observed test statistic, t < -2.01 or t > 2.01

Since the observed test statistic (0.7063) does not lie in the rejection region, we fail to reject H0 and conclude that there is no significant evidence that -100. That is, there is no significant evidence that the coefficient on FEMALE is different than -100