Question

A bolt manufacturer is very concerned about the consistency with which his machines produce bolts. The bolts should be 0.22 centimeters in diameter. The variance of the bolts should be 0.025. A random sample of 28 bolts has an average diameter of 0.23⁢cm with a standard deviation of 0.2478. Can the manufacturer conclude that the bolts vary by more than the required variance at α=0.01 level?

Step 1 of 5:

State the hypotheses in terms of the standard deviation. Round the standard deviation to four decimal places when necessary.

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:

Make the decision.to reject null hypothesis or fail to reject null hypothesis

Step 5 of 5:

What is the conclusion?

There is sufficient evidence that shows the bolts vary by more than the required variance.

OR

There is not sufficient evidence that shows the bolts vary by more than the required variance.

Answer 1

Claim: the manufacturer concludes that the bolts vary by more than the required variance.

Sample size = n = 28

Sample Standard deviation = s = 0.2478

Step 1: The null and alternative hypothesis is

Step 2:

Degrees of freedom = n - 1 = 28 - 1 = 27

Level of significance = 0.01

Critical value = 46.963 ( Using chi-square table)

Step 3:

Test statistic is

Step 4:

Test statistic > critical value we reject the null hypothesis.

Step 5:

There is sufficient evidence that shows the bolts vary by more than the required variance.