The quality department at Electro Tech is examining which of two microscope brands (Brand A or Brand B) to purchase. They have hired someone to inspect six circuit boards using both microscopes. Below are the results in terms of the number of defects (e.g., solder voids, misaligned components) found using each microscope.
Circuit Board Number of defects with Brand A Number of defects with Brand B
1.........................................12.............................................14
2..........................................8...............................................9
3.........................................16.............................................16
4.........................................14.............................................12
5..........................................9...............................................8
6.........................................13.............................................15
a. Specify the null and alternative hypotheses to test for differences in the defects found between the microscope brands.
b. At the 5% significance level, find the critical value(s) of the test. What is the decision rule?
c. Assuming that the difference in defects is normally distributed, calculate the value of the test statistic.
d. Based on the preceding results, is there a difference between the microscope brands?