Question

A carpenter is making doors that are 2058 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 39 doors is taken, and it is found that they have a mean of 2069 millimeters. Assume a population standard deviation of 24. Is there evidence at the 0.02 level that the doors are either too long or too short?

Step 1 of 3:

State the null and alternative hypotheses.

Step 2 of 3:

Find the P-value for the hypothesis test. Round your answer to four decimal places.

Step 3 of 3:

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

Answer 1

Solution:

Step 1 of 3:

This a right (One) tailed test.

The null and alternative hypothesis is,  

Ho: 2058

Ha: 2058

Step 2 of 3:

The test statistics,

Z =( - )/ (/n)

= ( 2069 - 2058 ) / ( 24 / 39 )

= 2.86

P-value = P(Z > z )

= 1 - P(Z < 2.86 )

= 0.0021

Step 3 of 3:

The p-value is p = 0.0021, and since p = 0.0021 < 0.02, it is concluded that the null hypothesis is rejected.

reject the null hypothesis.