Question

A lumber company is making boards that are 2716.0 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 23 boards is made, and it is found that they have a mean of 2714.9 millimeters with a standard deviation of 12.0. Is there evidence at the 0.1 level that the boards are either too long or too short? Assume the population distribution is approximately normal.

Step 1 of 5:

State the null and alternative hypotheses.

Step 2 of 5:

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

boards are either too long or too short? Assume the population distribution is approximately normal.

Step 3 of 5:

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

Step 4 of 5:

Determine the decision rule for rejecting the null hypothesis. Round your answer to three decimal places.

Step 5 of 5:

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

Answer 1

Step 1 of 5:

H0: Null Hypothesis : = 2716

HA: Alternative Hypothesis: 2716

Step 2 of 5:

n = sample size = 23

= sample mean = 2714.9

s = sample SD = 12

SE = s/

= 12/ = 2.5022

Test statistic is:

t = ( - )/SE

= (2714.9 - 2716)/2.5022 = - 0.4396

Step 3 of 5:

Two tail test

Step 4 of 5:

ndf = 23 - 1 = 22

= 0.10

From Table, critical value of t = - 1.321

Decision rule for rejecting the null hypothesis:

t < - 1.321

Step 5 of 5:

Since calculated value of t = - 0.4396 is greater than critical value of t = - 1.321, Fail to reject H0.

Conclusion:

There is no evidence at the 0.1 level that the boards are too long or too short.