Question

A carpenter is making doors that are 2058.0 millimeters tall. If the doors are too long they must be trimmed, and if they are too short they cannot be used. A sample of 18 doors is made, and it is found that they have a mean of 2044.0 millimeters with a variance of 144.00. Is there evidence at the 0.025 level that the doors are too short and unusable? 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.

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

1)

H0: = 2058

Ha: < 2058

2)

Test statistics

t = ( - ) / (S / sqrt(n ))

= ( 2044 - 2058) / ( sqrt(144) / sqrt ( 18) )

= -4.95

3)

This is one tailed test

4)

df = n - 1 = 18 - 1 = 17

t critical value at 0.025 significance level with 17 df = -2.110

Decision rule = Reject H0 if test statistics < -2.110

5)

Since test statistics value falls in rejection region, Reject the null hypothesis.