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 17 is made, and it is found that they have a mean of 2047.0 millimeters with a standard deviation of 27.0. 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. Find the value of the test statistic. Round your answer to three decimal places.

Answer 1

Solution :

This is the two tailed test,  

The null and alternative hypothesis is ,

H₀ :   = 2058.0

H_a :    2058.0

Test statistic = t =

= ( - ) / s / n

= (2047.0 - 2058.0) / 27.0 / 17

Test statistic = z = -1.680