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 18 is made, and it is found that they have a mean of 2043.0 millimeters with a standard deviation of 21.0. 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?

Answer 1

Since the population standard deviation is unknown hence we will be using T-distribution to conduct the test as:

The Hypotheses are:

rejection region:

Reject Ho at 0.01 level of significance if |T|>t_{0.01, 17 where} 17 is the degree of freedom which is calculated using T-table hown below.

Test Statistic:

P-value:

P-value is also computed using T table shown below as:

0.007<P-value<0.008

Conclusion:

Since P-value <<0.05 hence we reject the null hypothesis and conclude that there is enough evidence to support the claim.

T-table: