Consider a plastic injection molding process for a part with a target critical w

Question

Consider a plastic injection molding process for a part with a target critical width dimension of 100 and a historic standard deviation of 8. Periodically, clogs form in one of the feeder lines, causing the mean width to change, As a result, the operator periodically takes random samples of size four. A recent sample yielded a sample mean of 101.4. Conduct a hypothesis test to determine whether true mean width has increased. Use a significance level of 0.02 and the confidence interval approach for your test.

Explanation / Answer

Below are the null and alternate hypothesis,
H0: mu = 100
H1: mu > 100

Value of test statistics,
t = (101.4 - 100)/(8/sqrt(4)) = 0.35

degrees of freedom = 3

p-value = 0.3747

As p-value is greater than the significance level of 0.02, we fail to reject the null hypothesis.

Hence there is not enough evidence that the true mean has increased.

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