Question

A lumber company is making boards that are 2714.0 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 23 is made, and it is found that they have a mean of 2718.4 millimeters with a standard deviation of 10.0. 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?

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

Or

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

Answer 1

We go by the Z test:

As	Significance Level	SL	0.05
	So P value	P	0.95
	Z for 95%	Z	1.96
	Mean	M	2718.4
	Std Dev	S	10
	sample size	n	23
	Standard error = ?(s2/n)	SM	2.085144
	Board Length
	? = M + Z(sM)	Max	2722.487
	? = M - Z(sM)	Min	2714.313

Hence we can conclude that they are too long.

Hence

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