Question

A lumber company is making boards that are 2533.0 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 14 is made, and it is found that they have a mean of 2536.4 millimeters with a variance of 64.00. 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

Answer:

Step-by-step explanation:

$n = sample size =14\\Mean = x bar = 2536.4 mm\\Var = s^2 = 64\\Std dev =s =8\\\\Population mean = 2533.0\\Mean difference = 2536.4-2533 = 3.4\\Std error of sample = 8/sqrt 14 =2.14\\Test statistic = (3.4)/2.14) = 1.59$

Since sample size is small and population std dev is not known, t test should be used.

p value = 0.135849

Since p>0.05 we accept that samples have a mean equal to 2533mm

There is no sufficient evidence to support the claim that the boards are either too long or too short