INFERENTIAL STATISTICS AND FINDINGS 9
Inferential Statistics and Findings
QNT/561
Inferential Statistics and Findings
Hill AFB has seen a substantial decline in production for F-16 aircraft over the past two fiscal years. The problem is substantial enough to warrant research, analysis, and intervention in order to increase production rates back to baseline standards. In order to discover the root cause of the problem, 5 research questions have been developed that require inferential statistics to analyze their results.
Analysis of the data from the following 5 research questions includes the two-sample z-test of independent means as an inferential technique to analyze the data. The two sample z-test of independent means uses the standard normal distribution and was selected because the sample sizes are greater than 30 for each of the tests. The samples can be treated as independent because it is likely that the personnel (and other factors) involved have changed between 2012 and 2014, but are not dependent upon each other.
Application of Inferential Statistics
Analysis of each question was performed, with the results/application provided below.
RQ1: Did the rate of mechanical failures increase from FY2012 to FY2014?
Let µ1 represent the population mean number of mechanical failures per day for FY2012, and let µ2 represent the population mean number of mechanical failures per day for FY2014.
The sample data is:
The hypotheses are:
Null:
Alternative:
Assuming a 95% confidence level, the value of α = 0.05. The critical value for a left-tailed test with α = 0.05 is -1.6449.
The test statistic is:
The p-value which corresponds to a z-value of -5.1322 is 0.0000. Since the test statistic (-5.1322) is less than the critical value (-1.6449), the decision is to reject the null hypothesis. Alternatively, since the p-value (0.0000) is less than the value of α (0.05), the decision is to reject the null hypothesis.
The conclusion of the test is that there is sufficient evidence, at the 0.05 level of significance, to support the claim that the mean number of mechanical failures per day has increased from FY2012 to FY2014.
RQ2: Have material backorders increased from FY2012 to FY2014?
Let µ1 represent the population mean number of material backorders per day for FY2012, and let µ2 represent the population mean number of material backorders per day for FY2014.
The sample data is:
The hypotheses are:
Null:
Alternative:
Assuming a 95% confidence level, the value of α = 0.05. The critical value for a left-tailed test with α = 0.05 is -1.6449.
The test statistic is:
The p-value which corresponds to a z-value of -5.4106 is 0.0000. Since the test statistic (-5.4106) is less than the critical value (-1.6449), the decision is to reject the null hypothesis. Alternatively, since the p-value (0.0000) is less than the value of α (0.05), the decision is to reject the null hypothesis. The conclusion of the test is that there is sufficient evidence, at the 0.05 level of significance, to support the claim that the mean number of material backorders per day has increased from FY2012 to FY2014.
RQ3: Have labor hours per F-16 aircraft increased from FY2012 to FY2014?
Let µ1 represent the population mean number of labor hours per F-16 aircraft for FY2012, and let µ2 represent the population mean number of labor hours per F-16 aircraft per day for FY2014.
The sample data is:
The hypotheses are:
Null:
Alternative:
Assuming a 95% confidence level, the value of α = 0.05. The critical value for a left-tailed test with α = 0.05 is -1.6449.
The test statistic is:
The p-value which corresponds to a z-value of -4.0147 is 0.0000. Since the test statistic (-4.0147) is less than the critical value (-1.6449), the decision is to reject the null hypothesis. Alternatively, since the p-value (0.0000) is less than the value of α (0.05), the decision is to reject the null hypothesis. The conclusion of the test is that there is sufficient evidence, at the 0.05 level of significance, to support the claim that the mean number of labor hours per F-16 aircraft has increased from FY2012 to FY2014.
RQ4: Have labor hours per worker increased or decreased from FY2012 to FY2014?
Let µ1 represent the population mean number of labor hours per worker for FY2012, and let µ2 represent the population mean number of labor hours per worker per day for FY2014.
The sample data is:
The hypotheses are:
Null:
Alternative:
Assuming a 95% confidence level, the value of α = 0.05. The critical value for a left-tailed test with α = 0.05 is -1.6449.
The test statistic is:
The p-value which corresponds to a z-value of -7.3284 is 0.0000. Since the test statistic (-7.3284) is less than the critical value (-1.6449), the decision is to reject the null hypothesis. Alternatively, since the p-value (0.0000) is less than the value of α (0.05), the decision is to reject the null hypothesis. The conclusion of the test is that there is sufficient evidence, at the 0.05 level of significance, to support the claim that the mean number of labor hours per worker has increased from FY2012 to FY2014.
RQ5: Have employee engagement scores increased or decreased from FY2012 to FY2014?
Let µ1 represent the population mean employee engagement score for FY2012, and let µ2 represent the population mean employee engagement score for FY2014.
The sample data is:
Since the research question asks if the employee engagement scores have “increased or decreased”, this test could be performed as either a two-tailed or a one-tailed test. Since the mean value for FY2012 is already known to be greater than the mean value for FY2014, a more specific question would be “Have employee engagement scores decreased from FY2012 to FY2014”.
The hypotheses are:
Null:
Alternative:
Assuming a 95% confidence level, the value of α = 0.05. The critical value for a right-tailed test with α = 0.05 is 1.6449.
The test statistic is:
The p-value which corresponds to a z-value of 0.1161 is 0.4538. Since the test statistic (0.1161) is less than the critical value (1.6449), the decision is to fail to reject the null hypothesis. Alternatively, since the p-value (0.4538) is greater than the value of α (0.05), the decision is to fail to reject the null hypothesis. The conclusion of the test is that there is insufficient evidence, at the 0.05 level of significance, to support the claim that the mean employee engagement scores have decreased from FY2012 to FY2014.
Alternative Testing
Aside from the two-sample z-test of independent means being used as an inferential technique to analyze data, an alternative form of testing is the two sample t-test for independent means. Using the two sample t-test, there would be a slight change in the calculation of the test statistic, as the team would use a pooled standard deviation value. The critical value of the test statistic would also be slightly different from that of the z-test due to the number of degrees of freedom.
With such a large sample (n = 297 and n = 365), there would be virtually no difference in the conclusions of the tests. The reason that a sample size of 30 is generally considered to be sufficiently large enough for use of the z-statistic is because the t-distribution approaches the normal distribution as the sample size increases. Once the sample size reaches about n = 30, the difference between the two distributions becomes less significant (McClave et al., 2011). And the larger the sample size, the more indistinguishable the two distributions are from each other.
Conclusion
Analysis of the data from the 5 research questions included the two-sample z-test of independent means as an inferential technique to analyze the data. The z-test resulted in the probability that mechanical failure rates increased, material backorders increased, labor hours per F-16 aircraft increased, and labor hours per worker increased between FY2012 and FY2014. However, there is insufficient evidence to conclude that employee engagement scores decreased during the specified time. Accumulative conclusion of the data presented suggests that overall work has increased for the F-16 aircraft at Hill AFB, while employee engagement remains constant. This increased level of work may be a factor in increase production cycle times, resulting in late aircraft deliveries.
References
McClave, J., Benson, P., & Sincich, T. (2011). Statistics for Business and Economics, 11th ed. Boston, MA: Prentice Hall.