Question

A lumber company is making boards that are 2790 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 36 boards is taken, and it is found that they have a mean of 2785.5 millimeters. Assume a population standard deviation of 13. Is there evidence at the 0.1 level that the boards are too short and unusable?

Step 4 of 6:

Find the P-value of the test statistic. Round your answer to four decimal places

Answer 1

Solution :

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ = 2790
Alternative Hypothesis, Ha: μ < 2790

Rejection Region
This is left tailed test, for α = 0.1 and df = 35
Critical value of t is -1.306.
Hence reject H0 if t < -1.306

Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (2785.5 - 2790)/(13/sqrt(36))
t = -2.08

P-value Approach
P-value = 0.022457

P value = 0.0225

As P-value < 0.10, reject null hypothesis.

Please like if it helps me please please

Thank you so much