Question

A lumber company is making boards that are 2923.0 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 16 is made, and it is found that they have a mean of 2919.7 millimeters with a standard deviation of 8.0. 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. Is there sufficient evidence to support the claim that the boards are either too long or too short?

Answer 1

Solution :

= 2923.0

= 2919.7

s = 8.0

n = 16

This is the two tailed test .

The null and alternative hypothesis is ,

H₀ :    = 2923.0

H_a :     2923.0

Test statistic = t

= ( - ) / s / n

= (2919.7- 2923.0) / 8.0 / 16

= −1.65

Test statistic = t = −1.65

P-value = 0.1197

= 0.05  

P-value ≥

0.1197 ≥ 0.05

Do not reject the null hypothesis .

There is insufficient evidence to suggest that