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 :

= 2058

=2069

=24

n = 39

This is the right tailed test .

The null and alternative hypothesis is ,

H0 :   < 2058

Ha : >2058

Test statistic = z

= ( - ) / / n

= (2069 -2058) / 24 / 39

= 2.86

P(z > 2.86 ) = 1 - P(z < 2.86 ) = 1 -0.9979

P-value =0.0021

= 0.02

P-value <

0.0021 < 0.02

Reject the null hypothesis .

There is sufficient evidence to suggest that