Response to Student Benjamin Washburn
Your discussion on the reformulation of the hypothesis to increase the sample types is accurate. While investigating the effect of an acquisition strategy template on the time it takes to complete a document, you suggest that four contactors at Patuxent River be used. Whereas the reformulation brings out the effect of having more than one sample type, I think it fails to adequately answer part (a) of the question that requires a two-sample hypothesis test. Don't you think that for the part (a) you would have selected two of the contractors at Patuxent River? Let’s say 2.2 and 2.3 and investigated whether the average time of completing the document is the same or not. It, therefore, follows that your null hypothesis and alternate hypothesis does not address the two-sample hypothesis test.
Nonetheless, your type I and type II errors give a correct scenario pegged on your formulated null-hypothesis. It is however not clear on the effect of 0.01 and 0.02 p-values. Finally, your discussion does not bring out the applicability of the Turkey-Kramer test. Probably it is because of failing to separate the two-sample test and the four-samples in your discussion. A separation of the two-sample test and more than two-sample test specified in part (a) and (b) would make your discussion that generally demonstrates an understanding of the concept under discussion clearer.
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Response to Student Bradd Baldwin
I like how you have selected the samples. You choose to use sample products in real life with a disclaimer; the mercury direct fuel injection (DFI) oil and Quick Premium Plus TC-W3. Your research accurately meets the needs of the part (a) that requires the investigation of two samples. However, don't you think it would be more accurate to investigate whether the mean volume of the two types of one-gallon packaging is the same? Rather than subjecting it to a fixed capacity of 3.78 liters. I find it inaccurate to use a fixed volume.
Nonetheless, your discussion on type I and II are accurate based on the presented null-hypothesis. I also disagree with your explanation of the p –values. I think the p-values should indicate the percentage chance of committing type I or type II errors. As such, a p-value of 0.01 presents a 1% change while a p-value of 0.02 presents a 2percent chance. Finally, I agree with your use of the Turkey-Kramer test and the backing up of your discussion with a simulation. Just as a parting shot, why is the Turkey-Kramer test most appropriate for more than two sample-tests?