More than 200,000 people worldwide take the GMAT examination each year as they a
ID: 3135103 • Letter: M
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 and standard deviation about . One hundred students go through a rigorous training program designed to raise their GMAT scores.
Test the following hypotheses about the training program
in each of the following situations:
(a) The students' average score is . Is this result significant at the 5% level?
(b) The average score is . Is this result significant at the 5% level?
Both results are significant at . The test statistic corresponding to the first situation is , and the test statistic corresponding to the second situation is .
Both results are not significant at . The test statistic corresponding to the first situation is , and the test statistic corresponding to the second situation is .
The first result is not significant and the second result is, at .
Explanation / Answer
a)
Formulating the null and alternative hypotheses,
Ho: u <= 525
Ha: u > 525
As we can see, this is a right tailed test.
Getting the test statistic, as
X = sample mean = 541.4
uo = hypothesized mean = 525
n = sample size = 100
s = standard deviation = 100
Thus, z = (X - uo) * sqrt(n) / s = 1.64
Also, the p value is
p = 0.050502583
As P > 0.05, we FAIL TO REJECT THE NULL HYPOTHESIS.
IT IS NOT SIGNIFICANT. [ANSWER]
***********************************
b)
Formulating the null and alternative hypotheses,
Ho: u <= 525
Ha: u > 525
As we can see, this is a right tailed test.
Getting the test statistic, as
X = sample mean = 541.5
uo = hypothesized mean = 525
n = sample size = 100
s = standard deviation = 100
Thus, z = (X - uo) * sqrt(n) / s = 1.65
Also, the p value is
p = 0.049471468
As P < 0.05, we REJECT THE NULL HYPOTHESIS.
IT IS SIGNIFICANT. [ANSWER]
**************************************
Hence,
OPTION C: The test statistic corresponding to the first situation is z = 1.64, and the test statistic corresponding to the second situation is z = 1.65.
The first result is not significant and the second result is, at alpha = 0.05. [ANSWER, C]
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