Question

A can of soda is labeled as containing 13 fluid ounces. The quality control manager wants to verify that the filling machine is neither over-filling nor under- filling cans. complete (a)-(d)

a.Determine the null and alternative hypotheses that would be used to determine if the filling machine is calibrated correctly.

b.The quality control manager obtains a sample of 83 cans and measures the contents. The sample evidence leads the manager to reject the null hypothesis. Write a conclusion for this hypothesis test.

c. Suppose, in​ fact, the machine is not out of calibration. Has a Type I or Type II error been​ made?

d.Management has informed the quality control department that it does not want to shut down the filling machine unless the evidence is overwhelming that the machine is out of calibration. What level of significance would you recommend the quality control manager to​ use? Explain.

Answer 1

a. Determine the null and alternative hypotheses that would be used to determine if the filling machine is calibrated correctly.

Null hypothesis: H₀: The filling machine is calibrated correctly with a can of 13 fluid ounces.

Alternative hypothesis: H_a: The filling machine is not calibrated correctly with a can of 13 ounces.

H₀: µ = 13 versus H_a: µ ≠ 13

This is a two tailed test.

b. The quality control manager obtains a sample of 83 cans and measures the contents. The sample evidence leads the manager to reject the null hypothesis. Write a conclusion for this hypothesis test.

For this test, we reject the null hypothesis. This means, there is insufficient evidence to conclude that the filling machine is calibrated correctly with a can of 13 fluid ounces.

c. Suppose, in​ fact, the machine is not out of calibration. Has a Type I or Type II error been​ made?

We know that the type I error is the probability of rejecting null hypothesis when it is true. Also, type II error is the probability of do not rejecting null hypothesis when it is not true.

For the given test scenario, we reject the null hypothesis that filling machine is calibrated correctly, but in fact, the machine is not out of calibration. This is a type I error.

Answer: Type I error

d. Management has informed the quality control department that it does not want to shut down the filling machine unless the evidence is overwhelming that the machine is out of calibration. What level of significance would you recommend the quality control manager to​ use? Explain.

We will recommend 0.01 alpha level of significance for this test scenario, because for this small level of significance, we make more appropriate and reliable conclusions.