Question

Empathy: The Interpersonal Reactivity Index is a survey designed to assess four different types of empathy. One type of empathy, called Empathetic Concern, measures the tendency to feel sympathy and compassion for people who are less fortunate. The index ranges from

0

(less empathetic) to

28

(more empathetic). The following data, representing random samples of

15

males and

15

females, are consistent with results reported in psychological studies. Boxplots show that it is reasonable to assume that the populations are approximately normal. Can you conclude that there is a difference in mean empathy score between men and women? Let

μ1

denote the mean empathy score for men. Use the

=α0.10

level and the

P

-value method with the TI-84 Plus calculator.

Males
20	12	16	13	26	21	23	8
15	18	25	15	23	17	22

Females
20	26	25	28	24	16	19	20
23	21	23	15	26	19	25

Answer 1

Males	Females
20	20
12	26
16	25
13	28
26	24
21	16
23	19
8	20
15	23
18	21
25	23
15	15
23	26
17	19
22	25

Using Excel

data -> data analysis -> t-Test: Two-Sample Assuming Equal Variances

t-Test: Two-Sample Assuming Equal Variances
	Males	Females
Mean	18.26666667	22
Variance	26.78095238	14.57142857
Observations	15	15
Pooled Variance	20.67619048
Hypothesized Mean Difference	0
df	28
t Stat	-2.248496094
P(T<=t) one-tail	0.016300214
t Critical one-tail	1.312526782
P(T<=t) two-tail	0.032600428
t Critical two-tail	1.701130934

p-value = 0.0326 < alpha (0.10)

hence we reject the null hypothesis

we conclude that there is significant different in means