Question

In a study of the relationship between family size and school performance in junior high school, 25 children in “only child ” families had an average GPA (grade point average) of 2.82 with a standard deviation of 0.34, and 20 first-born children in two-child families had an average GPA of 2.96 with a standard deviation of 0.38. At the 0.05 level of significance, is the difference between these means significant?

1. You must state the null and alternative hypotheses.

2. Compute the test statistics and p-value.

3. State the decision and make the conclusion in the words of the problem.

Answer 1

Solution:

1.)

The hypothesis are

H0:  ₁ =  ₂

Ha : _1    2

2)

The test statistic t is given by

t =

where    denotes the pooled variance.

t =

=

= -1.303

Test statistic t = -1.303

Now we find the p value.

d.f. = n₁ + n₂ - 2 = 25  + 20 - 2 = 43

t = -1.303

sign in Ha indicates that " Two tailed test"

p value = 0.0998

3)

Decision: Fail to reject H₀

Conclusion: There is not sufficient evidence to conclude that the difference between these means significant.