A personality psychologist wanted to know if men and women differ in their sympa

Question

A personality psychologist wanted to know if men and women differ in their sympathy and compassion expressed to others. She gave a personality test to randomly selected men and women. One component of the test measured empathy, with higher scores indicating more empathy. The data are shown in the spreadsheet. Carry out a t-test on H0: M= W(population means for Men and Women are the same) vs. Ha: M W(population means for Men and Women differ) at the alpha=.05 level

1a) what is the observed value of t?

A) 2.48

B) 2.05

C) -2.48

D) -2.05

1b) what is the probability (P) value of the test ?

A) 0.02

B) 0.98

C) 0.05

D) 0.01

Explanation / Answer

We applied two-sample t-test using excel assuming equal variance and the results are as follows from where we have

1a) Observed value of t=-2.48

1b) p-value=0.0194=0.02

t-Test: Two-Sample Assuming Equal Variances Male Female Mean 17.86666667 21.8 Variance 23.83809524 13.88571429 Observations 15 15 Pooled Variance 18.86190476 Hypothesized Mean Difference 0 df 28 t Stat -2.480268002 P(T<=t) one-tail 0.009704507 t Critical one-tail 1.701130934 P(T<=t) two-tail 0.019409014 t Critical two-tail 2.048407142

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