Question

A lumber company is making boards that are 2951.0 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 20 boards is made, and it is found that they have a mean of 2947.4 millimeters with a standard deviation of 14.0. Is there evidence at the 0.025 level that the boards are too short and unusable? Assume the population distribution is approximately normal. Step 1 of 5: State the null and alternative hypotheses. Answer 2 Points Tables Keypad

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ = 2951
Alternative Hypothesis, Ha: μ < 2951

Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (2947.4 - 2951)/(14/sqrt(20))
t = -1.150

This is left tailed test,

for α = 0.025 and df = 19
Critical value of t is -2.093.
Hence reject H0 if t < -2.093

Fail to reject Null hypothesis