Question

A bolt manufacturer wants to investigate the machine that produces bolts with a diameter of 0.2 centimeters. If the variance of the diameters is equal to 0.025, then the machine is working as expected. A random sample of 11 bolts has a standard deviation of 0.18. Does the manufacturer have evidence at the α=0.05 level that the variance of the bolt diameters is more than required? Assume the population is normally distributed. Step 2 of 5 : Determine the critical value(s) of the test statistic. If the test is two-tailed, separate the values with a comma. Round your answer to three decimal places.

Step 3 of 5: Determine the value of the test statistic. Round your answer to three decimal places.

Step 4 of 5: Reject or fail to reject null hypothesis?

Step 5 of 5: What is the conclusion? Is there sufficient evidence or not enough sufficient evidence?

Answer 1

The provided sample variance is s^2 = 0.0324 and the sample size is given by n = 11.

(1) Null and Alternative Hypotheses

The following null and alternative hypotheses need to be tested:

Ho:= 0.025

Ha: > 0.025

This corresponds to a right-tailed test, for which a Chi-Square test for one population variance will be used.

(2) Rejection Region

Based on the information provided, the significance level is α=0.05, and the the rejection region for this right-tailed test is

(3) Test Statistics

The Chi-Squared statistic is computed as follows:

(4) Decision about the null hypothesis

Since it is observed that = 12.96 < = 18.307 , it is then concluded that the null hypothesis is not rejected.

(5) Conclusion

It is concluded that the null hypothesis Ho is not rejected. Therefore, there is not enough evidence to claim that the population variance is greater than 0.025, at the 0.05 significance level.