Question

A premium golf ball production line must produce all of its balls to 1.615 ounces in order to get the top rating (and therefore the top dollar). Samples are drawn hourly and checked. If the production line is tested with a statistical significance level of more than 1%, it must be shut down and repaired. This hour’s sample of 18 balls has a mean of 1.641 ounces and a sample standard deviation of 0.065 ounces. Do you shut down the line?

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ = 1.615
Alternative Hypothesis, Ha: μ ≠ 1.615

Rejection Region
This is two tailed test, for α = 0.01 and df = 17
Critical value of t are -2.898 and 2.898.
Hence reject H0 if t < -2.898 or t > 2.898

Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (1.641 - 1.615)/(0.065/sqrt(18))
t = 1.697

P-value Approach
P-value = 0.1079
As P-value >= 0.01, fail to reject null hypothesis.

There is no need to shut down the line.