Question

A lumber company is making boards that are 2709 millimeters tall. If the boards are too long they must be trimmed, and if they are too short they cannot be used. A sample of 38 boards is taken, and it is found that they have a mean of 2711.5 millimeters. Assume a population variance of 196. Is there evidence at the 0.05 level that the boards are too long and need to be trimmed?

Step 1 of 6:

State the null and alternative hypotheses.

Step 2 of 6:

Find the value of the test statistic. Round your answer to two decimal places.

Step 3 of 6:

Specify if the test is one-tailed or two-tailed.

Step 4 of 6:

Find the P-value of the test statistic. Round your answer to four decimal places.

Step 5 of 6:

Identify the level of significance for the hypothesis test.

Step 6 of 6:

Make the decision to reject or fail to reject the null hypothesis

Answer 1

1 Tailed Z test, Single Mean

Given: = 2709 mm, = 2711 mm, = 196, therefore = 14, n = 38, = 0.05

(1) The Hypothesis:

H0: = 2709: The mean height of the boards is equal to 2709 mm.

Ha: > 2709: The mean mean height of the boards is greater than 2709 mm.

(2) The Test Statistic: The test statistic is given by the equation:

Z observed = 1.10

(3) Tail of the Test: This is a 1 tailed test (Right tailed)

(4) The p Value: The p value for Z = 1.10, p value = 0.1357

(5) The Level of significance, = 0.05

(6) The Decision Rule: If P value is < , Then Reject H0.

The Decision: Since P value (0.1357) is > (0.05) , We Fail To Reject H0.

__________________________________________________________

The Conclusion: There isn't sufficient evidence at the 0.05 significance level to conclude that the mean height of the boards is greater than 2709 mm.