Howdy! I'm Professor Curtis of Aspire Mountain Academy here with more statistics homework help. Today we're going to learn how to use one-way ANOVA for hypothesis testing of cigarette filters. Here's our problem statement: Refer to the accompanying data table which shows the amounts of nicotine (in milligrams per cigarette) of king-sized cigarettes, 100-mm menthol cigarettes and 100-mm non-menthol cigarettes. The king-sized cigarettes are non-filtered, while the 100-mm menthol cigarettes and the 100-mm non-menthol cigarettes are filtered. Use a 5% significance level to test the claim that the three categories of cigarettes yield the same mean amount of nicotine. Given that only the king-sized cigarettes are not filtered, do the filters appear to make a difference?
OK, the first part of this problem is asking us to determine the null and alternative hypotheses. With one-way ANOVA, this is pretty much set in stone. The null hypothesis will always be that all of your population parameters are equal, and the alternative hypothesis will be that at least one of those parameters is different from the others. So I'm going to select those here in the drop down menus for each of these hypotheses. Nice work!
Now the next part asks us to find the F statistic. To do that, I'm going to use StatCrunch. To use StatCrunch, I need to get the data in. First I'm going to click on this icon and open my data in StatCrunch, and I'm going to move this window so we can see everything that we're doing.
OK, now inside StatCrunch I have my data. So I go to Stat –> ANOVA –> One-Way. Here in the options window, I'm going to select all of my columns, and I press Compute!. And here we have in the results window the ANOVA table which lists my F statistic. I'm asked to round that to four decimal places. Nice work!
The next part asks me to find the P-value, which is right next door to my F statistic in my ANOVA table. Again I'm asked around to four decimal places. Nice work!
The next part asks, “What is the conclusion for this hypothesis test?” Well, my P-value here in this example is about 1%. I'm asked to use a 5% significance level. 1% is less than 5%, so I'm within the region of rejection, and therefore I'm going to reject the null hypothesis. And of course when we reject the null hypothesis, there's always sufficient evidence. Fantastic!
And now the final part of the problem asks, “Do the filters appear to make a difference?” Well, let's look at the mean values here from our column statistics. We see that the king size and the 100-millimeter menthol cigarettes are more or less in the same ballpark. There's a little bit of a separation there. The filtered non-menthol cigarettes, however — these are really different from the other two. So let's look at our answer options and see what we get.
Do the filters appear to make a difference? Well, I would claim by looking at these mean values that they do make a difference, so answer options A and C we're not going to select. Answer option B (the results are inconclusive) — I don't think the results are completely inconclusive.
So that leaves us with answer option D: “Given that the king-sized cigarettes have the largest mean” — and here we see that they do — “it appears that the filters do make a difference, although this conclusion is not justified by the results from analysis of variance.” That's very true. You're going to need to do some other statistical analysis to justify it. But just based on what we see here, the two filtered varieties do have a slightly lower mean value than the non-filtered king-sized cigarettes. And so we're going to select answer option D. Nice work!
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Frustrated with a particular MyStatLab/MyMathLab homework problem? No worries! I'm Professor Curtis, and I'm here to help.