Question

A company claims to manufacture paper clips with a standard deviation of less than 0.12g. A
set of 71 paper clips has a sample standard deviation of 0.10 g. Is the claim supported by the test?  

Answer 1

Solution:

Given:

Claim: paper clips has a standard deviation of less than 0.12g.

Sample size = n = 71

sample standard deviation = s = 0.10 g.

Step 1) State H0 and H1:

Vs

Step 2) Test statistic:

Step 3) Critical value:

df = n - 1 = 71 - 1 = 70

level of significance = 0.05

Since this is left tailed test, find area = 1-0.05= 0.95

Chi-square critical value = 51.739

Step 4) Decision Rule:

Reject null hypothesis H0, if Chi square test statistic < Chi-square critical value = 51.739, otherwise we fail to reject H0.

Since Chi square test statistic = < Chi-square critical value = 51.739, we reject null hypothesis H0.

Step 5) Conclusion:

At 0.05 significance level, we have sufficient evidence to support the claim that paper clips has a standard deviation of less than 0.12g.