In Problems 21–32, state the conclusion based on the results o...

Question

In Problems 21–32, state the conclusion based on the results of the test.

For the hypotheses in Problem 19, the null hypothesis is rejected.

Accepted Answer

Hello. In this video, we are told that a researcher investigates the average number of customer complaints per week received by 3 different service centers, Center A, Center B, and Center C. A random sample of weekly complaints was recorded over several weeks for each center as shown below. At the 0.05 significance level, tests that claim that the that the mean number of weekly complaints is the same across the three service centers. If the null hypothesis is rejected, identify which center appears different and describe how. So, let's go ahead and start this problem by setting up our hypothesis. Now, we want to test the claim that the mean number of weekly complaints is the same across the three service centers. So, are no hypothesis in this case. Is going to be that the mean with respect to center a. The mean with respect to center B and the mean with respect to center C are all going to be equal to each other. And the alternate hypothesis states. That at least one. Is different So that's going to be our null and alternate hypothesis for this test. Now, what we are going to do next is we are going to want to calculate the mean for each of the centers. Now, the mean for center A is going to be the sum of all the values of the complaints divided by the number of data points there is available. That is going to be 8 + 7 + 9 + 6 + 8, divided by the total amount of points, which is going to be 5. And that is going to give us a mean of 7.6%er A. Repeating this process for the mean of center B, we get 5 + 6 + 4 + 5 + 6 divided by 5, and that is going to give us a mean of 5.2. And finally, for center C, we get that the mean is 12 + 14 + 13 + 15 + 16 divided by 5, and that gives us a mean of 14.0. Now, in order to approach this type of test, we are going to use a one-sided, a one-way Enova test. The Enova test tests whether 3 or more group means are equal, and a low P-value suggests that at least 1 is different. So In order to perform the Enova test, we are going to use a calculator or online software. But by performing an Enova test, we get an F statistic of 60.8, and we get a P value that is less than 0.0001. Now, if we compare this P value to the significance level we are working with, which is 0.05, notice that the P value is less than our significance level. What this means is that we are going to reject. Our no hypothesis. Furthermore, what this means is that at least one of the center's means are going to be statistically different from the others. Now, in order to figure this out, we are just going to compare the means that we calculated earlier, but notice that center C has the highest mean amongst the three centers. So, what this means is that center C is different by having the highest average number of complaints amongst the three centers. And with that being said, the solution to this problem is going to be B. So, I hope this video helps you in understanding how to approach this problem, and we will go ahead and see you all in the next video.

In Problems 21–32, state the conclusion based on the results of the test.
For the hypotheses in Problem 19, the null hypothesis is rejected.

Key Concepts

Null Hypothesis (H0)

Hypothesis Testing and Conclusion

Significance Level and Decision Rule

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