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Answer:
The null hypothesis failed to be rejected (P-value=0.014).
Step-by-step explanation:
This is a hypothesis test for the population mean.
The null and alternative hypothesis are:
The significance level is α=0.01.
The sample has a size n=20.
The sample mean is M=9.
As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=7.5.
The estimated standard error of the mean is computed using the formula:
Then, we can calculate the t-statistic as:
The degrees of freedom for this sample size are:
This test is a right-tailed test, with 19 degrees of freedom and t=2.385, so the P-value for this test is calculated as (using a t-table):
As the P-value (0.014) is bigger than the significance level (0.01), the effect is not significant.
The null hypothesis failed to be rejected.