Question

You are the CEO at a nail polish manufacturing plant. You want to determine if the nail polish filling process is in control. The process requires NO corrective action if the correct amount of nail polish is 368 grams. For studying this, a random sample of 25boxes, weighing each one. The sample mean is 372.5 and the process standard deviation (population) is 15. Is there evidence that the weight is different from 368 grams? You have selected α = 0.01 as your significance level.

3.1 Hypothesis are:

3.2 The calculated Z value is:

3.3 The critical Z value is:

3.4 The result is:

3.5 The conclusion is:

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ = 368
Alternative Hypothesis, Ha: μ ≠ 368

2)
Test statistic,
z = (xbar - mu)/(sigma/sqrt(n))
z = (372.5 - 368)/(15/sqrt(25))
z = 1.5

3)

Rejection Region
This is two tailed test, for α = 0.01
Critical value of z are -2.576 and 2.576.
Hence reject H0 if z < -2.576 or z > 2.576

4)

As the value of test statistic, z is outside critical value range, fail to reject the null hypothesis

5)

There is not sufficient evidence to conclude that the weight is different from 368 grams