Question

1. Suppose we have the following information on GMAT scores for business and non-business majors:

Business Majors                      Non-Business Majors

n₁ = 8                                      n₂ = 5

X₁ = 545                                  X₂ = 525

s₁ = 120                                   s₂ = 60

1. Using a 0.05 level of significance, test to see whether the population variances are equal.
2. Using a 0.05 level of significance, test the clam that average GMAT scores for business majors is above the average GMAT scores for non-business majors in the population. Assume unequal population variances.

Answer 1

a) Using a 0.05 level of significance, test to see whether the population variances are equal.

This can be done by using F test

Let's use minitab:

Step 1) Click on Stat >>>Basic Statistics >>>2-Variances ...

Fill the necessary information and then click on Option again fill the necessary information.

Look the following image:

Then click on OK again Click on OK , so we get the following output:

p-value = 0.198

Since p-value > 0.05 we fail to reject the equality assumption of two populations.

So that the variances of the two populations are not different.

b) Using a 0.05 level of significance, test the clam that average GMAT scores for business majors is above the average GMAT scores for non-business majors in the population. Assume unequal population variances.

Here the null hypothesis(H₀ ) and the alternative hypothesis (Ha ) are as follow:

Null hyypothesis :

Alternative hypothesis :

Now lets test the equality of two means using unpooled t test, because here we need to assume unequal population variances.

Level of significance = = 0.05

Therefore level of confidence = 100 - 5 = 95%

Let's used minitab :

Steps 1) Click on Stat>>>Basic Statistics>>>2-Sample t...

Steps 1) Click on summarized data and then fill the required information in the boxes : look the following picture.

step 3) Click on Option, Look the following image :

then click on OK again click on OK

So we get the following output

From the above N output p-value = 0.349

Test statistic = T value = 4.40

Decision rule: 1) If p-value <= level of significance (alpha) then we reject null hypothesis

2) If p-value > level of significance (alpha) then we fail to reject null hypothesis.

Here p value = 0.349 > 0.05 so we used second rule.

That is we fail to reject null hypothesis

Conclusion: At 5% level of significance there are not sufficient evidence to say that average GMAT scores for business majors is above the average GMAT scores for non-business majors in the population.