Answer:
The p-value for this test is 0.1375.
Step-by-step explanation:
A student believes that the average grade on the statistics final examination was 87. The student wants to test whether the average is different from 87 at 90% level of confidence.
At the null hypothesis, we test if the average is 87, that is:
At the alternate hypothesis, we test if the average is different from 87, that is:
The test statistic is:
We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.
In which X is the sample mean, is the value tested at the null hypothesis,
is the standard deviation of the sample and n is the size of the sample.
87 is tested at the null hypothesis:
This means that
The average grade in the sample was 83.96 with a standard deviation of 12. Sample of 36
This means that
Value of the test-statistic:
Pvalue:
Probability of the sample mean differing of 87, which means that we have a two-tailed test, with t = -1.52 and 36 - 1 = 35 degrees of freedom.
With the help of a calculator, the pvalue is of 0.1375.
The p-value for this test is 0.1375.