Question

A lumber company is making boards that are 2729.0 millimeters tall. If the boards are too long they must be trimmed, and if the boards are too short they cannot be used. A sample of 30 is made, and it is found that they have a mean of 2725.1 millimeters with a standard deviation of 12.0. A level of significance of 0.05 will be used to determine if the boards 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 :   = 2729.0

Ha :    2729.0

Test statistic = t =

= ( - ) / s / n

= (2725.1- 2729.0) / 12.0 / 30

Test statistic = t = -1.780

degrees of freedom = n - 1 = 30 - 1 = 29

P(t < -1.780) = 0.0428

P-value = 2 * P(t < -1.780)

P-value = 2 * 0.0428

P-value = 0.0856

= 0.05  

P-value >

Fail to reject the null hypothesis .