Question

More than 200,000 people worldwide take the GMAT examination each year as they apply for MBA programs. Their scores vary normally with mean about u= 525 and standard deviation about sigma= 100. One hundred students go through a rigorous training program designed to raise their GMAT scores. Test the hypotheses. H sub 0: u= 525. H sub A: u > 525


Answer the following question based from the given stated.
a) The students' score is x = 541.4. Is this result significant at the 5% level? b) The average score is x = 541.5. Is this result significant at the 5% level? c) What conclusions may you draw by comparing the answers to parts a and b?

Answer 1

For letter a
$z= \frac{x-u}{SD \sqrt{n} } \\ z= \frac{541.4-525}{100 \sqrt{100} } \\ z=1.64$
Looking up z=1.64, its equivalent is 0.4495
∈=0.5+0.4495
∈=0.9495
As 0.95>0.9495, we cannot reject the null hypothesis, and the result is not significant.
b.)$Z= \frac{(mean-u)SD}{ \sqrt{n} } \\ Z= \frac{(541.5-525)100}{ \sqrt{100} } \\ Z=1.65$
Looking it up, P(Z>1.65)=0.0505. The result is not significant.
c. The p values are larger than the accepted level of 0.05, which is why the null is rejected. As we cannot reject the null, it is to be accepted that the mean score is 525. This then requires more statistical testing to be done to prove the null.