Use the following problem outline to conduct all the appropriate hypothesis test
ID: 3289518 • Letter: U
Question
Use the following problem outline to conduct all the appropriate hypothesis tests below. Include the p-Value for each test. Use the data and analysis that are shown on the next page (Last Page). Include Levene's Test and the appropriate T-test. There should be two complete hypothesis tests on your Scantron. One Levene's Test and one T-test. Be sure to put your written answers OVER ON your Scantron form, NOT HERE please and thank you! In planning the processes to be incorporated into a new manufacturing facility, engineers have proposed two possible assembly procedures for one of the phases in the production sequence. Production workers have taken part in preliminary tests, with data on the number of units produced in one hour for 31 workers using Process A and 21 workers using Process B. Given the data and analyses on the next page, use the 0.05 level of significance and the appropriate statistical test to determine whether the average number of units produced by workers using Process A could be different from the average number of units produced by workers using Process B. Follow the outline below to do the appropriate hypothesis tests. This is just an outline. Use this outline ON YOUR SCANTRON. If you do not understand the instructions, ask the instructor any questions about the instructions you might have. Good Luck. I. HYPOTHESES II. DECISION RULE WITH REJECTION REGION(S) Include a fully labeled graphic of the rejection region and the decision rule in complete sentences alpha (a) and the appropriate degrees of freedom (df) for the tests. III. TEST STATISTIC IV. CONCLUSION Using a complete sentence, please indicate the conclusion you should draw from your analysis. V. IMPLICATION(S) Using a complete sentence, please indicate the implications of your analysis. VI. Also include the p-Value for each respective test by stating is value, for example, p- Value = _____Explanation / Answer
Levine’s test
I. Null Hypothesis (Ho): 1^2 = 2^2
Alternative Hypothesis (Ha): 1^2 2^2
II. Alpha = 0.05
Degrees of freedom, df (numerator) = 30
Degrees of freedom, df (denominator) = 20
Using F-tables, the critical value is
F (0.05, 30, 20) = 2.0391
If F-statistics > F-critical value, we reject Ho.
III. Test Statistics
F = 1.745
IV. Since F-statistics is less than the critical value, we fail to reject Ho.
V. Hence, we cannot conclude that the variance of process A is different from the variance of process B.
VI. P-value = 0.0983
T-test assuming unequal variances
I. Null Hypothesis (Ho): µ1 = µ2
Alternative Hypothesis (Ha): µ1 µ2
II. Alpha = 0.05
Degrees of freedom, df = 31+ 21 = 52
Using t-tables, the critical value is
t (0.05/2, 52) = 2.0096
If t-statistic > t-critical value or t-statistic < -t-critical value, we reject Ho.
III. Test Statistics
t = 1.0591
IV. Since test statistics lie within the critical value, we fail to reject Ho.
V. Hence, we cannot conclude that the average of process A is different from the average of process B.
VI. P-value = 0.29476