Question

The inmates at McAlester Prison, Oklahoma, make an average of 437 license plates per day. The warden feels that their production is too low and suspects that the inmates are wasting a lot of time on the job. In order to test his opinion, he obtains the mean license plate production for a sample of nine other prisons in the state. The data are listed below:

452

440

464

461

435

439

449

459

446

can the warden support the research hypothesis that the inmates of McAlester Prison are less productive in making license plates than are the inmates at other prisons at the 0.005 significance level? Justify your answer.

Answer 1

1. We want to test that the inmates of McAlester Prison are less productive in making license plates than are the inmates at other prisons at the 0.005 significance level.

Here we are going to use one sample t test because population standard deviation is unknown.

Null hypothesis H₀: µ = 437

Alternative hypothesis H₁: µ < 437

2. This is one sided test.

We have given Population mean µ = 437

Sample mean (X) = 449.44

Sample standard deviation (S) = 10.38

Sample size (n) = 9

3. The one sided t critical value at degrees of freedom n-1 = 8 and α=0.005

T_{8, 0.005} = -3.355 (from statistical table)

Rejection region: Reject H₀ if test statistics t < -3.355.

4. Test statistics (t) = (X - µ) / (S/ √n)

t = (449.44 - 437)/ (10.38/sqrt(9))

Test statistics t = 3.60

5. Decision: t statistics = 3.60 > t_{8, 0.005} = -3.355 that means t statistics value not fall in rejection region. So we failed reject null hypothesis at 0.005 level of significance.

6. P value = P(t < 3.60) = T.DIST(3.6,8,TRUE)) = 0.9965…. (using Excel)

P value = 0.9965 > 0.005 so we do not reject null hypothesis at 0.005 alpha level.

7. We can conclude that, there is not sufficient evidence of 0.005 level of significance that the inmates of McAlester Prison are less productive in making license plates than are the inmates at other prisons