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 34 doors is taken, and it is found that they have a mean of 2048 millimeters. Assume a population variance of 441. Is there evidence at the 0.1 level that the doors are too short and unusable?

Step 4 of 6:

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

Answer 1

Solution :

This is the two tailed test,  

The null and alternative hypothesis is ,

H0 :   = 2058

Ha :    2058

Test statistic = z

= ( - ) / / n

= (2048 - 2058) / 21 / 34

Test statistic = z = -2.78

P(Z < -2.78) = 0.0027

P-value = 2 * 0.0027

P-value = 0.0054

= 0.1

P-value <

Reject the null hypothesis .

There is sufficient evidence to suggest that the doors are too short and unusable