Question

A psychologist found that a common perception among both men and women is that women tend to be more empathetic than men. She set out to determine if there were data to support this claim. She administered a diagnostic that measures the level of empathy on a scale from 0–28. Below are the scores for a random sample of 16 men and and a random sample of 16 women.

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

Women
22 20 26 25 28 24 16 19 20 23 21 23 15 26 19 25

(a) Do the data suggest women are more empathetic than men. Test at the 5% significance level.

(b) Explain the meaning of the P-value in the context of this test.

(c) What would it mean to commit a Type I error in the context of this test?

(d) What would it mean to commit a Type II error in the context of this test?

Answer 1

a)From the given data

(1) Null and Alternative Hypothesis:

H0: women are not more empathetic than men

H1: women are more empathetic than men

i.e.

Thus we conclude that women are more empathetic than men

b)

Thus we conclude that women are more empathetic than men

c) Type I error:
We find that women are more empathetic than men
when the reality is that women are not more empathetic than men

d) Type II error:

We find that women are not more empathetic than men
when the reality is that women are more empathetic than men