How to do this hypothesis testing question?
A business student claims that, on average, an MBA student is required to prepare more than five cases per week. To examine the claim, a statistics professor asks a random sample of 10 MBA students to report the number of cases they prepare weekly. The results are exhibited here. Can the professor conclude at the 5% significance level that the claim is true, assuming that the number of cases is normally distributed with a standard deviation of 1.5?
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A business student claims that, on average, an MBA student is required to prepare more than five cases per week. To examine the claim, a statistics professor asks a random sample of 10 MBA students to report the number of cases they prepare weekly. The results are exhibited here. Can the professor conclude at the 5% significance level that the claim is true, assuming that the number of cases is normally distributed with a standard deviation of 1.5?
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1 Answer
Yes, the student's claim appears to be true based upon this one sample. See explanation.
Explanation:
For this problem, it is helpful to determine the null hypothesis and the alternate hypothesis. Since the student claims that an MBA student prepares an average of more than 5 cases per week, we can specify our null hypothesis
The alternate hypothesis
Since we are told that the number of cases is normally distributed with a standard deviation
To proceed, we need to know the mean of the cases from our sample of 10:
We can now calculate the z-test value according to the z-test formula:
In this formula:
Our z-test score is about 2.11. Now, since our alternate hypothesis is that we are expecting the population mean to be more than 5 cases per week, we are looking for a right-tail probability (since we are looking at an alternate hypothesis that specifies values greater than 5).
According to a z-score table, the left-tail (aka cumulative from negative infinity) probability associated with a z-score of 2.11 is about 0.9826. Thus, the right-tail probability
At a 5% (0.05) significance level, our