A lumber company is making boards that are 2609.0 millimeters tall. If the board

Question

A lumber company is making boards that are 2609.0 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 2605.7 millimeters with a variance of 144.00. 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

Explanation / Answer

Data:    

n = 16   

= 2609   

s = 12   

x-bar = 2605.7   

Hypotheses:   

Ho: = 2609   

Ha: 2609   

Decision Rule:   

= 0.1   

Degrees of freedom = 16 - 1 = 15

Lower Critical t- score = -1.753050325

Upper Critical t- score = 1.753050325

Reject Ho if |t| > 1.753050325

Test Statistic:   

SE = s/n = 12/16 = 3

t = (x-bar - )/SE = (2605.7 - 2609)/3 = -1.1

p- value = 0.288672958   

Decision (in terms of the hypotheses):

Since 1.1 < 1.75305 we fail to reject Ho

Conclusion (in terms of the problem):

There is no sufficient evidence that the boards are too long or too short.

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