Question

A bolt manufacturer wants to investigate the machine that produces bolts with a diameter of 0.18 centimeters. If the variance of the diameters is equal to 0.015, then the machine is working as expected. A random sample of 26 bolts has a standard deviation of 0.1806. Does the manufacturer have evidence at the α=0.1 level that the variance of the bolt diameters is more than required? Assume the population is normally distributed.

Step 1 of 5: State the null and alternative hypotheses. Round 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 Step 5 of 5: What is the conclusion?

Answer 1

1)
Below are the null and alternative Hypothesis,
Null Hypothesis: ^2 = 0.015
Alternative Hypothesis: ^2 > 0.015

2)
Rejection Region
This is two tailed test, for alpha = 0.05 and df = 25
Critical value of ^2 are 37.652
Hence reject H0 if ^2 < 13.12 or ^2 > 40.646

3)
Test statistic,
^2 = (n-1)*s^2/^2
^2 = (26 - 1)*0.0326/0.015
^2 = 54.333

4)
P-value Approach
P-value = 0.0006
As P-value < 0.05, reject the null hypothesis.

5)
Conclusion
There is sufficient evidence to conclude that the variance of the bolt diameters is more than required