The MAT Testing Center creates standardized exams. Recently, the Testing Center
ID: 3160114 • Letter: T
Question
The MAT Testing Center creates standardized exams. Recently, the Testing Center in Washington State received complaints saying that the mean time required to complete the exam exceeds the advertised mean of 50 minutes. Before responding, employees at the Testing Center plan to test this claim using a level of significance of 0.05 and a sample of 100 nursing students. The sample (of 100 nursing students) produced a mean of 52.5 minutes. Based on the previous studies, assume that the population standard deviation is known to be 9 minutes. Is the claim correct? Can we conclude that the mean time required to complete the exam exceeds the advertised mean of 50 minutes? Justify your answer. Make sure to state the null and the alternative hypotheses.
Explanation / Answer
Formulating the null and alternative hypotheses,
Ho: u <= 50
Ha: u > 50
As we can see, this is a right tailed test.
Thus, getting the critical z, as alpha = 0.05 ,
alpha = 0.05
zcrit = + 1.644853627
Getting the test statistic, as
X = sample mean = 52.5
uo = hypothesized mean = 50
n = sample size = 100
s = standard deviation = 9
Thus, z = (X - uo) * sqrt(n) / s = 2.777777778
Also, the p value is
p = 0.002736602
As z > 1.645, and P < 0.05, we REJECT THE NULL HYPOTHESIS.
There is significant evidence that the mean time required to complete the exam exceeds the advertised mean of 50 minutes. [CONCLUSION]
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