Chancerossman 2015 iscam iii inve this test statistic

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Chance/Rossman, 2015 ISCAM III Investigation 1.9 77 This test statistic is simply the application of the z-score from the previous investigation, and you will interpret it as “how many standard deviations the observed proportion p ˆ lies from the hypothesized process proportion.” With th e two-sided p-value, we are interested in how often we will obtain a p ˆ value as far from the hypothesized probability in either direction . Due to the symmetry of the normal curve, this only involves doubling one of the tail probabilities. (i) Based on the test statistic value you calculated, does the sample proportion appear to be extreme under the null hypothesis? (j) Use technology (e.g., Normal Probability Calculator applet) to determine the approximation to the two-sided p-value with the normal distribution. Is your p-value consistent with your sketch in (f)? (k) Provide a one-sentence interpretation of this p-value. (l) Based on this p-value, will you reject the null hypothesis at the 5% level of significance? (m) Do you think the researchers are pleased by the lack of significance in this test? Explain, in the context of this study, why such a result might be good news for them. (n) Does this mean the researchers can conclude that they have proven that children do not have a preference between candy and toys? Explain.
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Chance/Rossman, 2015 ISCAM III Investigation 1.9 78 Study Conclusions If we define S to be the probability that, when presented with a choice of candy or a toy while trick- or-treating, a child chooses the toy, and if we assume the null hypothesis (H 0 : S = 0.5) is true, the above calculations tell us that we would observe at most 135 children choosing candy (at least 149 choosing toy) or at most 135 of the 284 children choosing the toy in about 40% of samples. Thus, this is not a surprising outcome when S = 0 .5. We fail to reject the null hypothesis and conclude that it’s plausible that children are equally split in preferring the toy or the candy. We do have some cautions with this study as it was conducted in only a few households in Connecticut, a convenience sample, so we cannot claim that these results are representative of c hildren in other neighborhoods. We also don’t know if the children found the toys “novel” and whether their preference for toys could decrease as the novelty wears off (or if “better” candy choices were offered). Furthermore, when the children approached the door they were asked their age and gender, and for a description of their Halloween costume. The researchers caution that that this may have cued the children that their behavior was being observed (even though their responses were recorded by another research member who was out of sight) or that they should behave a certain way. Still, these researchers were optimistic that alternatives could be presented to children, even at Halloween, to lessen their exposure to large amounts of candy.
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