Answer :
Using the t-distribution, it is found that the correct option is:
0.005 < P-value < 0.01, reject the null hypothesis.
What are the hypothesis tested?
At the null hypothesis, it is tested if the mean of a given population is equal to 85, that is:
[tex]H_0: \mu = 85[/tex]
We have a left-tailed test, hence, at the alternative hypothesis, it is tested if the mean of the population is less than 85, that is:
[tex]H_1: \mu < 85[/tex]
What is the decision?
The test statistic is of t = -3.018.
Using a t-distribution calculator, with test statistic t = -3.018, 13 - 1 = 12 df and a significance level of 0.01, it is found that the p-value for a left-tailed test is of 0.0051.
The p-value is less than 0.01, hence the null hypothesis is rejected and the correct option is:
0.005 < P-value < 0.01, reject the null hypothesis.
More can be learned about the t-distribution at https://brainly.com/question/16313918