Start a Minitab session. If you are unable to complete this lab assignment in on
ID: 3221372 • Letter: S
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Start a Minitab session. If you are unable to complete this lab assignment in one Minitab session, save the project as Lab 8-3-2. Never use a period as pun of the project name; since Minitab uses the period to attach the file type to the file name. Then at your next Minitab session, you may open this Lab 8-3-2. MPJ project and continue to work where you left off previously. In a union contract negotiating session, management wanted to reduce the number of union assemblers and replace them with robots. The union argued that although the robots could assemble the parts more quickly than human workers, the human workers produced a more uniform product. The union argued that the experienced workers could see small imperfections and correct these problems, but the robots were unable to do this. Management agreed to test this claim before purchasing the robots. Nine randomly selected products made by the union workers were measured for their smoothness and the results were: 23.1, 24.2, 22.9, 23.6, 23.5, 24.0, 23.7, 23.6 and 23.2. At a test site where robots were already in use. 12 products made by robots were randomly selected and their smoothness was measured with the following results: 22.8, 23.7, 24.1, 23.8, 23.1, 24.1, 22.9 23.1, 23.7, 22.9, 23.6 and 23.5. Past experience has shown that for products made both by union members and by robots, the smoothness scores of these products are normally distributed. Test the hypothesis that the standard deviation of all products assembled by union workers is less than the standard deviation of all products assembled by robots. Did the union save the jobs of some of its members? Use a 0.05 level of significance. Brand name producers of aspirin claim that one advantage of their aspirin over generic aspirin is that brand name aspirin is much more consistent in the amount of active ingredient used. This in turn means that users can expect the same results each time they use the brand name aspirin, while the effects of the generic aspirin can be a lot more variable. A random sample of 200 brand name aspirin tablets had a mean and standard deviation of active ingredient of 325.01 and 10.12 mg. A second independent sample of 180 generic aspirin tablets was measured for the amount of active ingredient, and the mean standard deviation were 323.47 and 11.43 mg. Given that the amount of active ingredient is normally distributed for both the brand name and the generic aspirin, do these data support the brand name producers claim? Let alpha = 0.025.Explanation / Answer
Solution:-
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: Aspirin< Generic
Alternative hypothesis: Aspirin > Generic
Note that these hypotheses constitute a one-tailed test. The null hypothesis will be rejected if the mean difference between sample means is too small.
Formulate an analysis plan. For this analysis, the significance level is 0.025. Using sample data, we will conduct a two-sample z-test of the null hypothesis.
Analyze sample data. Using sample data, we compute the standard error (SE) and the z statistic test statistic (z).
SE = sqrt[(s12/n1) + (s22/n2)]
SE = 1.1126
DF = 359.65
D.F = 360
z = [ (x1 - x2) - d ] / SE
z = 1.384
where s1 is the standard deviation of sample 1, s2 is the standard deviation of sample 2, n1 is the size of sample 1, n2 is the size of sample 2, x1 is the mean of sample 1, x2 is the mean of sample 2, d is the hypothesized difference between population means, and SE is the standard error.
The observed difference in sample means produced a z statistic of 1.384. We use the z Distribution Calculator to find P(z > 1.384) = 0.0838
Therefore, the P-value in this analysis is 0.0838.
Interpret results. Since the P-value (0.084) is greater than the significance level (0.025), we cannot reject the null hypothesis.
From the above test we do not have sufficient evidence in the favor of the claim that Aspirin is more more consisitent in constituent than generic aspirin.
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