Question

t-Test: Two-Sample Assuming Unequal Variances

A two-sample test for means was conducted to test whether the mean number of movies watched each month differed between males and females. The Excel Data Analysis tool results are shown below.

	Female	Male
Mean	5.6	7.5
Variance	6.267	21.833
Observations	10	10
Hypothesized Mean Difference	0
DF	14
T Stat	-1.133
P(T<=t) One-Tail	0.138
t Critical One-Tail	1.76
P(T<=t) Two-Tail	0.276
t Critical Two-Tail	2.144

a. Explain how to use this information to draw a conclusion if the null hypothesis is H₀: µ_F - µ_M <= 0. Clearly state the correct critical value and p-value and your conclusion.

b. Explain how to use this information to draw a conclusion if the null hypothesis is H₀: µ_F - µ_M >= 0. Clearly state the correct critical value and p-value and your conclusion.

c. Explain how to use this information to draw a conclusion if the null hypothesis is H₀: µ_F - µ_M = 0. Clearly state the correct critical value and p-value and your conclusion.

Answer 1

a) This is a one-tailed test, however since this is a lower tailed test, the critical value will be negative

P(T<=t) One-Tail

0.138

t Critical One-Tail

-1.76

The hypothesis cannot be rejected as the p-value is not significant

b) This is a one-tailed test

P(T<=t) One-Tail

0.138

t Critical One-Tail

1.76

The hypothesis cannot be rejected as the p-value is not significant

c) This is a two-tailed test

P(T<=t) Two-Tail	0.276
t Critical Two-Tail	2.144

The hypothesis cannot be rejected as the p-value is not significant