Question

A lumber company is making boards that are 2563.0 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 15 is made, and it is found that they have a mean of 2560.5 millimeters with a standard deviation of 8.0. A level of significance of 0.1 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?

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

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

Answer 1

This is the two tailed test .

The null and alternative hypothesis is

H₀ : = 2563

H_a : 2563

Test statistic = t

= ( - ) / s / n

= (2560.5 - 2563) / 8 / 15

= -1.210

Test statistic = -1.210

df = 14

P-value = 0.2462

= 0.1

P-value >

Fail to reject the null hypothesis .

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