Question

5.A recent study was done comparing the IQ scores of women and men. In a sample of 22 women, the average IQ score was 100.6 with a sample standard deviation of 7.3, and for a sample of 13 men, the average IQ score was 101.3 with a sample standard deviation of 9.8. Use a 0.01 level of significance to test the claim that the average IQ score for women and men is the same.

Answer 1

Solution

Given ,

   = 100.6 , = 101.3

s₁ = 7.3 , s₂ = 9.8

n₁ = 22 , n₂ = 13

The hypothesis are

H0:  ₁ =  ₂

Ha : _1    2

The test statistic t is given by

t =  

=

= -0.241

Test statistic t = -0.241

Now ,

d.f. = n₁ + n₂ - 2 = 22 + 13 - 2 = 33

Two tailed test

So , p value = 0.81

p value is greater than given 0.01 level of significance

Fail to reject H₀

There is not sufficient evidence to reject the claim that  the average IQ score for women and men is the same.