Question 4.DS.9: Art Snakeoil, the tool manufacturer’s sale representative, i......
Art Snakeoil, the tool manufacturer’s sale representative, insists that the tools he sells are more accurate than those of his competitor and he challenges the Purchasing Department to compare the fastener tools from two plants. Plant “A” where the competitor’s tools are used and Plant “B” where the Art Snakeoil’s tools are used. Fastening defect data has been collected in both plants on a monthly basis for the past 3 years. However, Plant “B” started collecting data 4 months later than
Plant “A.” The monthly number of defects was recorded as:
The Purchasing Department notes that an initial review of this data as shown above provides insufficient information to make a buying decision. Therefore, Purchasing requested that the Engineering Department provide a statistical analysis to properly evaluate this comparison by following the format below:
a. State the appropriate hypothesis
b. Test the hypothesis using α = 0.05
c. Construct a 95% confidence interval on the defect comparison
| Plant A Fastening Defects (Competitor’s Tools) | Plant B Fastening Defects (Snakeoil’s Tools) |
| n_{1}=36 | n_{2}=32 |
| \overline{x}_{1}=16.1 | \overline{x}_{2}=14.3 |
| S_{1}=4.3 | S_{2}=5.1 |
Approach:
1. H_{0}: μ_{1} = μ_{2}
2. H_{a}: μ_{1} > μ_{2}
3. α = 0.05 Art Snakeoil, the manufacturer’s rep, requests analysis at α = 0.05 (Z_{0.05} = 1.645)
4. n_{1} and n_{2} are Large (n_{1} and n_{2} > 30)
5.n_{1} = 36 and n_{2} = 32 where n is large, σ can be estimated by S
6. To disprove H_{0} : (\overline{x}_{1} − \overline{x}_{2} ) > 0
Use the Upper Limit (U.L.) to describe the comparison difference confidence interval.
7. Note that (\overline{x}_{1} − \overline{x}_{2} ) = 16.1−14.3 = 1.8
Displaying the data above yields:
We must, therefore, conclude that the test statistic (\overline{x}_{1} − \overline{x}_{2} ) = 1.8 is less than the U.L. = 1.895 and therefore is in the acceptance region and we therefore accept H_{0}. Hence, at the significance level of α = 0.05, there is no statistical difference between the creation of fastening defects of the two representative tool data sets. However, when the numbers are as “close” as shown, further testing and analysis is typically warranted.
