You Are A Recent Graduate And Have Been Hired By John Jolly

You Are A Recent Graduate And Have Been Hired By John Jolly To Run An

John Jolly, owner of John's Jolly Oil Change, is experimenting with a new oil change process and wants to determine if it takes less time than the old process. Over a week, he collected and compared sample times for both processes. Using the data provided, a t-test for independent samples was conducted at a significance level (α) of 0.05 to evaluate the hypothesis about the population means. The results included a p-value, which John misinterpreted as "9" and questioned, asking about the "E-05" at the end.

Paper For Above instruction

The primary goal of the analysis was to assess whether the new oil change process is more time-efficient compared to the traditional method. The initial hypotheses set for this statistical test are oriented towards determining a significant difference in mean times between the two processes, which is integral for making informed managerial decisions about adopting the new procedure.

Formally, the null hypothesis (H₀) states that there is no difference in the mean time taken by the new and old processes (μ₁ = μ₂), implying that the new process does not save time. The alternative hypothesis (H₁) posits that the new process takes less time than the old process (μ₁

Analyzing the results, the p-value is crucial. The report indicates a p-value reported as "9" with an "E-05" at the end. The notation "E-05" refers to scientific notation—specifically, 9 × 10^{-5}. Therefore, the p-value is 0.00009. When rounded to three decimal places, the p-value remains 0.000. Since this p-value is substantially below the significance level α of 0.05, it indicates a statistically significant result.

Contrary to John’s initial suspicion that the p-value might suggest non-significance, the data strongly support rejecting the null hypothesis. The very small p-value signifies that the difference in mean times is unlikely to have occurred by chance alone, providing strong evidence that the new process is indeed faster.

However, it is important to clarify what statistical significance does and does not imply. The results do not "prove" that the new process always takes less time in every situation or for every oil change. Rather, they indicate that, based on the sample data and within the limits of statistical inference, there is sufficient evidence to support that the new process reduces time compared to the old process under similar conditions.

In conclusion, the statistical analysis demonstrates that the new oil change process significantly decreases the time required. It is essential for John to understand that the result is robust evidence supporting the effectiveness of the new process but not an absolute guarantee for all scenarios. Proper implementation, continuous monitoring, and further testing can help ensure ongoing efficiency gains.

References

• Field, A. (2018). Discovering Statistics Using IBM SPSS Statistics. Sage Publications.
• Gravetter, F. J., & Wallnau, L. B. (2016). Statistics for the Behavioral Sciences. Cengage Learning.
• Moore, D. S., & McCabe, G. P. (2017). Introduction to the Practice of Statistics. W. H. Freeman.
• Tabachnick, B. G., & Fidell, L. S. (2013). Using Multivariate Statistics. Pearson Education.
• Levin, J., & Rubin, D. (2004). Statistics for Management. Pearson Education.
• Higgins, J. P. T., & Green, S. (2011). Cochrane Handbook for Systematic Reviews of Interventions. The Cochrane Collaboration.
• Larson-Hall, J. (2010). A Guide to Doing Statistics in Second Language Research Using SPSS. Routledge.
• Salkind, N. J. (2017). Statistics for People Who (Think They) Hate Statistics. Sage Publications.
• Field, A., Miles, J., & Field, Z. (2012). Discovering Statistics Using R. Sage Publications.
• Myers, R. H., Well, A. D., & Lorch, R. F. (2017). Elementary Statistics. Pearson.