State study on labor reported that one-third of full-time teachers in the state also worked part-time at another job. For those teachers, the average number of hours worked per week at the part-time job was 13. After an increase in state teacher salaries, a random sample of 400 teachers who worked part-time at another job was selected. The average number of hours worked per week at the part-time job for the teachers in the sample was 12.5 with a standard deviation of 6.5 hours. Is there convincing statistical evidence, at the level of α=0.05, that the average number of hours worked per week at part-time jobs decreased after the salary increase?
(A) No. The p-value of the appropriate test is greater than 0.05.
(B) No. The p-value of the appropriate test is less than 0.05.
(C) Yes. The p-value of the appropriate test is greater than 0.05.
(D) Yes. The p-value of the appropriate test is less than 0.05.
(E) Not enough information is given to determine whether there is convincing statistical evidence
answer a show work, please

From the solution to the question that we have here, the answer is A. There is no convincing evidence that the hours worked decreased after the increase in salary.

The hypothesis formulation

H0: u = 13

H1: u < 13

sample size n = 400

bar x = 12.5

mean = 13

How to solve for the t test statistics

[tex]t = \frac{x-u}{s/\sqrt{n} } \\\\t = \frac{12.5-13}{6.5/\sqrt{400} } \\[/tex]

= -1.5388

degree of freedom: 400 -1 = 399

∝ = 0.05

Find the p value

p(t < -1.5385)

= 0.062

The p value is greater than the level of significance. We therefore fail to reject the null hypothesis.