Question

A lumber company is making doors that are 2058.0 millimeters tall. If the doors are too long they must be trimmed, and if the doors are too short they cannot be used. A sample of 20 is made, and it is found that they have a mean of 2047.0 millimeters with a standard deviation of 30.0. A level of significance of 0.1 will be used to determine if the doors are either too long or too short. Assume the population distribution is approximately normal. Is there sufficient evidence to support the claim that the doors are either too long or too short?

A. There is sufficient evidence to support the claim that the doors are either too long or too short.

B. There is not sufficient evidence to support the claim that the doors are either too long or too short.

Answer 1

Solution:

This a right (One) tailed test.

The null and alternative hypothesis is,  

Ho: 2058

Ha: 2058

The test statistics,

t = ( - )/ (s/)

= ( 2047 - 2058 ) / ( 30 /20 )

= -1.640

P-value = 0.059

The p-value is p = 0.059 < 0.1, it is concluded that the null hypothesis is rejected.

There is sufficient evidence to support the claim that the doors are either too long or too short.

Option A is correct.