Meticulous Drill & Reamer (MD&R) specializes in drilling and boring precise holes in hard metals (e.g., steel alloys, tungsten carbide, and titanium). The company recently contracted to drill holes with 3-centimeter diameters in large carbon-steel alloy disks, and it will have to purchase a special drill to complete this job. MD&R has eliminated all but two of the drills it has been considering: Davis Drills’ T2005 and Worth Industrial Tools’ AZ100. These producers have each agreed to allow MD&R to use a T2005 and an AZ100 for one week to determine which drill it will purchase. During the one-week trial, MD&R uses each of these drills to drill 31 holes with a target diameter of 3 centimeters in one large carbon-steel alloy disk, then measures the diameter of each hole and records the results. MD&R’s results are provided in the table that follows and are available in the file *MeticulousDrills*.

MD&R wants to consider both the accuracy (closeness of the diameter to 3 centimeters) and the precision (the variance of the diameter) of the holes drilled by the T2005 and the AZ100 when deciding which model to purchase.

In making this assessment for MD&R, consider the following four questions:

- Are the holes drilled by the T2005 or the AZ100 more accurate? That is, which model of drill produces holes with a mean diameter closer to 3 centimeters?
- Are the holes drilled by the T2005 or the AZ100 more precise? That is, which model of drill produces holes with a smaller variance?
- Conduct a test of the hypothesis that the T2005 and the AZ100 are equally precise (that is, have equal variances) at a=0.05. Discuss your findings.
- Which drill do you recommend to MD&R? Why?

__Initial post prompt:__ Your Managerial Report serves as your initial post to the discussion forum. After responding to the requirements posed by the Managerial Report, also provide an example in your career in which you believe one of the lessons learned from the Case has been/could be applicable. Alternatively, if you don’t have/foresee direct experience relevant to your current position, what type of scenario can you anticipate occurring where you can utilize one of the lessons learned from examining this case?

__Response post prompt:__ Consider Managerial Reports posted by two of your peers. One or both of your responses may be to Managerial Reports for a case problem different from your own. Think critically and ask open-ended questions. If you agree, consider their position and expand upon their ideas. Provide an additional perspective. If you disagree, provide your reasoning. Always be professional and courteous in your responses.

Post by classmate 1

To first find which hole drilled by the T2005 or AZ100 is more accurate, we use the data given and first find the mean of each drill. **The mean for a hole drilled by a T2005 is 3.0223. The mean for a hole drilled by a AZ100 is 3.0229**. Next we use these means to find each drills absolute deviation by subtracting each mean from the target diameter of 3. When we get our values, **a T2005 absolute deviation is .0223 and for a AZ100 drill is .0229**. From this we see a T2005 has a smaller difference and the mean diameter is closer to 3cm. The company can conclude from this information that a T2005 drill would be more accurate in drilling a target diameter of 3 and should consider this drill for accuracy.

Question 2 asks us to find which drill would then be more precise by finding the smaller variance of the two chosen drills. **The variance for a T2005 drill is 0.0127 and the variance for a AZ100 drill is .0362. **The information tells us that a T2005 has a smaller variance and would produce more precise holes. MD&R should consider purchasing the T2005 for this reason.

Using a level of significance of .05 we can conduct a test of the hypothesis that the T2005 and the AZ100 are equally precise. The null hypothesis for the test is the models T2005 and AZ100 are equally precise and the alternative hypothesis is that the models T2005 and AZ100 are not equally precise. In excel we compute a two-sample F-test for variances to find the test statistic and p-value of the two drills. **Our chart shows a F-test statistic of 0.35 and one tailed p-value of .0027. **Because this is a two tailed test we must then multiply the one tailed p-value of .0027 by 2, to equal** a p-value of a two-tailed test .0054**. The p-value for our two-tailed test of .0054 is less than the level of significance so we would reject the null hypothesis and conclude that the T2005 and AZ100 are NOT equally precise.

If I were to recommend a drill to purchase for MD&R, I would choose the T2005 because it is able to provide more accurate and precise holes for drilling.

I can think of many ways this could apply to my career in healthcare. Often, we have vendors come to our unit to teach us about new products and provide in-services on how to use them. The information from this chapter could be very helpful for Nurses or Doctors who are introduced to new products but want to decide which product to use based on their accuracy and precision. These key factors for products would be very important to know when considering new medical equipment to introduce to our practice.

Post by classmate 2

**Are the holes drilled by the T2005 or the AZ100 more accurate? Which model produces holes with a mean of 3 centimeters**

In order to find which holes were more accurate and consistent, I had to find the mean diameter. For the T2005 and AZ100, I had to find the sum of all the trials and divide them by 31. This result gave me a mean of 3.022 for the T2005 and a mean of 3.023 for the AZ100. Then I subtracted each by 3 centimeters giving me .022 and .023 respectively. The T2005 produced more holes with a mean of 3 centimeters than the AZ100.

**Are the holes drilled by the T2005 or the AZ100 more precise? That is, which model of drill produces holes with a smaller variance?**

To figure out which holes drilled by the T2005 or the AZ100, I had to find the standard deviation of each and divide that be the degrees of freedom. Based on my calculations, I found that the T2005 had a variance of .0127 and the AAZ100 had a variance of .0362. The T2005 had a smaller variance, showing that it is more precise by consistently drilling holes closer to 3 centimeters.

**Conduct a test of the hypothesis that the T2005 and the AZ100 are equally precise (that is, have equal variances) at . Discuss your findings.**

I ran a hypothesis test that the T2005 and the AZ100 are equally precise at drilling 3-centimeter holes based on variance. My alternative hypothesis is that the two variances are not equal one another. My T-Stat was determined by dividing the variance of the T2005 by the variance of the AZ100 resulting in .35. My F-Critical 2 tailed score was found to be .54, the .35 t-stat is less than the .54 f-critical. Therefore, we must reject that the null hypothesis that the T2005 and the AZ100 have equal variances and accept the alternative hypothesis that the two are not equal.

**Which drill do you recommend to MD&R? Why?**

In my opinion, I would recommend the T2005 to MD&R as this drill had a smaller variance on the size of the holes that were drilled as well as consistently drilled holes closer to the 3-centimeter mark that was wanted by MD&R.

In my professional fundraising experience, I have not had to use these calculations. However, in situations similar to this case where a company is trying to find a consistent product or tool to use, I do think that finding the variance and hypothesis testing is useful as it will help a company produce more accurate and consistent results.

Reference

Anderson, D. R., Sweeney, D. J., Williams, T. A., Camm, J. D., Cochran, J. J., (2021). Modern Business Statistics with Microsoft Office Excel (7th ed.) Cengage.

October 7, 2022