Question

A lumber company is making boards that are 2997.0 millimeters tall. If the boards are too long they must be trimmed, and if they are too short they cannot be used. A sample of 22 boards is made, and it is found that they have a mean of 2995.6 millimeters with a standard deviation of 9.0. Is there evidence at the 0.1 level that the boards are too short and unusable? Assume the population distribution is approximately normal.

Step 4 of 5 :  

Determine the decision rule for rejecting the null hypothesis. Round your answer to three decimal places.

Answer 1

Solution :

= 2997.0

=2995.6

= 9.0

n = 22

This is the left tailed test .

The null and alternative hypothesis is ,

H0 :    = 2997.0

Ha :     2997.0

Test statistic = z

= ( - ) / / n

= (2995.6 -2997.0) /  9.0 / 22

= -0.73

Test statistic = z = -0.73

P(z > ) = 1 - P(z < -0.73 ) =  

P-value =0.233

= 0.01

P-value >

0.233 > 0.01

Fail to reject the null hypothesis .

There is insufficient evidence to suggest that