Question

Consider an engine parts supplier and suppose they determined that the variance of all cylindrical engine parts diameters produced by the current machine is .007. To reduce this variance, a new machine is designed. A random sample from the new machine is taken of 25 parts, which have a variance of .0046. At the 1% significance level, can we conclude that the new machine produces a smaller diameter variance? Please show all work hand written.

Answer 1

Solution:

Given:

Population Variance =

Sample size = n = 25

Sample variance = s² = 0.0046

We have to test if  the new machine produces a smaller diameter variance.

Level of significance = 0.01

thus

Step 1) State H0 and H1:

Vs

Step 2) Test statistic:

Chi square test statistic for variance

Step 3) Critical value:

df = n - 1= 25 - 1 = 24

Left tail area = 0.01

Thus to find Chi-square critical value using CHi-square table, find right tail = 1 - 0.01 = 0.99

Chi-square critical value = 10.856

Step 4) Decision Rule:

Reject null hypothesis H0, if Chi square test statistic < Chi-square critical value =10.856, otherwise we fail to reject H0.
Since Chi square test statistic = > Chi-square critical value =10.856, we fail to reject H0.

Step 5) Conclusion:

At 0.01 level of significance, we do not have sufficient evidence to conclude that the new machine produces a smaller diameter variance.

That is: the new machine does not produce a smaller diameter variance.