Hw9Sols - STAT 350 Assignment 9 Solutions (50 points) 1....

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STAT 350 Assignment 9 Solutions (50 points) 1. (2) (a) H 0 : µ A = µ B = µ C ; where µ i = average strength of wood of Type i. (2) (b) When a null hypothesis is not rejected in an ANOVA test it can often be good news. When there is no significant difference between two populations (types of beams in this case), you are then free to use other factors when making decisions about the populations. For instance, in this exercise, the choice is narrowed to Type A or B (both of which were shown by the ANOVA test to be superior in strength to Type C). To make the final decision (between A and B), we might use another factor, such as the cost of each type of beam, as a factor in deciding between them (since the ANOVA test shows no significant difference in their strengths). (2) (c) This is similar to pat (b), except now there is no significant difference between the strengths of any of the three beams, so another factor (e.g., cost) can be used to make a decision about which one to use. 4. (4) (Give full credit if they have mentioned that the repeated sampling from the same item will result in a smaller “Within variation”, or a smaller “between variation”, e ither is fine). There are dangers in using repeated measurement of the same item instead of truly replicating an experimental result. When using the same item multiple times you are assessing the effect of the experimental factor on only that one item. You have not determined how the experimental factor effects different items. Thus, you will not be able to draw inferences about the effect of the factor on the entire population of items. Also, since one might expect a single item to respond more similarly to multiple experimental treatments than different items might respond, the measure of variation “within samples” may be underestimated. The result of this is an inflated value of the F test statistic, resulting in an artificia lly sma ll p-value. So, one might conclude that there is a significant
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Hw9Sols - STAT 350 Assignment 9 Solutions (50 points) 1....

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