Separate and pooled variance Tests

A survey is conducted to see whether male and female drivers differ in the number of kilometers they drive per day. 19 males and 19 females were randomly selected in the survey and the followings are the results:

Males:

Sample Mean = 29.63 kilometers

Sample Variance = 453.13

Females:

Sample Mean = 30.52 kilometers

Sample Variance = 182.59

Test whether male and female drivers differ in the number of kilometres they drive per day. In other words test the following hypotheses:

H₀: ₁ - ₂ = 0

H₁: ₁ - ₂ 0

Assume population variances are not equal.

Use d.f. = 30 and alpha of 10% to conduct the test.

a) What is the critical value for this test?

b) What is the Decision Rule? (e.g. Reject the null if the test stat is < or > ???)

c) What is the Test Statistic?

d) What is the conclusion?

SHOW WORKING OUT PLEASE THANK YOU!