Two canned packaging machine are being tested for their effect on the shelf life of a processed food product. Machine 1 had a standard deviation of 38.7 over a sample of 20 batches, and machine 2 had a standard deviation of 21.8 over a sample of 25 batches. Assume that the shelf lives are normally distributed. Is there evidence at the 1% level of significance to support the claim that food made with machine 2 has a different standard deviation than with machine 1?

1. The correct null hypothesis and alternate hypothesis are:

2. For above hypothesis testing, what the test statistic should you use:

A: T-test

B: Z-test

C: F-Test

D: Chi-square Test

3. For above question, the value of the test statistic is:

A: 3.15

B: 2.78

C: 2.99

D: 2.66

4. The critical threshold for two-tailed 1% significance is the same as for a one-tailed test at 0.5% significance. Both can be found using a calculator. We want to know the probability of our ratio being farther into the right-tail than the threshold value, so we found the value should be:

A: 2.65

B: 3.09

C: 2.76

D: 3.02

5. Look at our test statistic and compare it with the threshold value, we :

A: cannot reject the null hypothesis at the 1% level of significance.

B: can reject the null hypothesis at the 1% level of significance.

6. Alternatively, we could calculate the actual significance level (P-value) , using a spreadsheet (or calculator) to find the probability that a ratio as large or larger than ours would occur by chance.

A: 0.44% one-tailed probability, which is the same as a 0.88% two-tailed probability.

B: 0.35% one-tailed probability, which is the same as a 0.70% two-tailed probability.

C: 0.41% one-tailed probability, which is the same as a 0.82% two-tailed probability.

D: 0.28% one-tailed probability, which is the same as a 0.56% two-tailed probability.