SCENARIO 10-12 A quality control engineer is in charge of the manufacture of USB flash drives.Two different processes can be used to manufacture the flash drives.He suspects that the Kohler method produces a greater proportion of defects than the Russell method.He samples 150 of the Kohler and 200 of the Russell flash drives and finds that 27 and 18 of them, respectively, are defective. If Kohler is designated as "Group 1" and Russell is designated as "Group 2," perform the appropriate test at a level of significance of 0.01.
-Referring to Scenario 10-12, the null hypothesis should be rejected.

Question

Quizplus · Accepted Answer

To perform the appropriate test in this scenario, we need to use a hypothesis test for the difference in two population proportions.

The null hypothesis is that there is no difference in the proportion of defects between the two groups:

H0: p1 - p2 = 0

The alternative hypothesis is that the proportion of defects is greater in the Kohler group:

Ha: p1 > p2

where p1 is the proportion of defects in the Kohler group and p2 is the proportion of defects in the Russell group.

Using the given sample data, we can calculate the sample proportions and the test statistic:

p1 = 27/150 = 0.18
p2 = 18/200 = 0.09
pooled sample proportion: p = (27+18)/(150+200) = 0.132
standard error: se = sqrt(p*(1-p)*(1/150+1/200)) = 0.038
test statistic: z = (p1-p2)/se = (0.18-0.09)/0.038 = 2.37

The critical value for a one-tailed test at a significance level of 0.01 is 2.33. Since the calculated test statistic (2.37) is greater than the critical value (2.33), we reject the null hypothesis.

Therefore, the correct answer is A. We can perform a hypothesis test for two proportions with a significance level of 0.01. The null hypothesis is that there is no difference in the proportion of defects between the two groups, while the alternative hypothesis is that the Kohler method produces a greater proportion of defects than the Russell method. Using a calculator or statistical software, we can calculate the test statistic as 2.172 and compare it to the critical value of 2.575. Since the test statistic is less than the critical value, we fail to reject the null hypothesis. Therefore, we do not have enough evidence to conclude that the Kohler method produces a greater proportion of defects than the Russell method.

SCENARIO 10-12 a Quality Control Engineer Is in Charge of the Manufacture