Question

3. A manufacturing company that produces shafts claims that one of the machined shafts has a diameter variance no larger than 0.0002 in'. A random sample of 10 shafts is collected and measured resulting in a sampled variance of 0.0003 in'. Assuming normality in the diameter measurements, is there significant evidence to refute the company's claim? Use a level of significance a = 0.05. Start your solution by clearly stating the null and alternative hypotheses, show all your calculations and then clearly state the criterion used to arrive to the conclusion. State clearly whether it is possible to refute or not the company's claim. (30 pts.).

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: σ^2 = 0.0002
Alternative Hypothesis, Ha: σ^2 < 0.0002

Rejection Region
This is left tailed test, for α = 0.05 and df = 9
Critical value of Χ^2 is 3.325
Hence reject H0 if Χ^2 < 3.325

Test statistic,
Χ^2 = (n-1)*s^2/σ^2
Χ^2 = (10 - 1)*0.0003/0.0002
Χ^2 = 13.5

P-value Approach
P-value = 0.8587
As P-value >= 0.05, fail to reject null hypothesis.

It is not possible to reute company claim