Of the 432 subjects asked the allow version 189

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“forbid” version, 161 favored the forbidding of communist speeches. Of the 432 subjects asked the “allow” version, 189 favored allowing the speeches. Construct a segmented bar graph for these data and comment on whether you believe the p-value for this table will be larger or smaller than that in (e). Explain your reasoning. Analysis (a) The observational units in this study are the statistics students. The explanatory variable is the word choice in the question they responded to (categorical) and the response variable is whether their response was in favor of the speeches (“yes” with the allow question and “no” with the forbid question, categorical). (b) This was an experiment because the word choice in the question was randomly assigned to the students. Presumably the instructor mixed up the order of the questionnaires prior to passing them out to the students. This is important to equalize other variables between these two groups such as political inclinations and gender. The students did not know that there were two different forms of the questions, so the study was blind. If they had realized that the instructor was focusing on how they responded to the two words, they probably would have responded differently eliminating any subconscious effect of the word choice. (c) Two-way table, with the explanatory variable, word choice, as the column variable, and defining a “success” to mean that the student is in favor of such speeches:
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Chance/Rossman, 2015 ISCAM III Example 3.1 244 Allow Forbid Total Success 8 12 20 Failures 3 2 5 Total 11 14 25 (d) Here is the segmented bar graph, with word choice along the horizontal axis, and success defined as favoring the speeches (yes to the allow question and no to the forbid question). We see that most of these students were in favor of the speeches (80%). There was a slight tendency for those responding to the forbid question to appear more in favor (more likely to say no, do not forbid the speeches), 0.857 versus 0.727. However, the distribution within the bars look fairly similar and the association does not appear to be strong. (e) The null hypothesis will be that there is no effect due to wording of the question. So if S allow is the probability someone says “yes” to the allow question and if S forbid is the probability someone says no to the forbid question: H 0 : S allow S forbid = 0 and based on the prior research: H a : S allow S forbid < 0 Fisher’s Exact Test indicates how often we expect to see as few as 8 or fewer successes in the allow group (equivalently, at least as many as 12 successes in the forbid group). So if we define X to be the number in the allow group in favor of the speeches, X follows a hypergeometric distribution with N = 25, M = 20, and n = 11. The p-value will be P(X d 8). ¸ ¸ ¹ · ¨ ¨ © § ¸ ¸ ¹ · ¨ ¨ © § ¸ ¸ ¹ · ¨ ¨ © § ² ¸ ¸ ¹ · ¨ ¨ © § ¸ ¸ ¹ · ¨ ¨ © § ¸ ¸ ¹ · ¨ ¨ © § ² ¸ ¸ ¹ · ¨ ¨ © § ¸ ¸ ¹ · ¨ ¨ © § ¸ ¸ ¹ · ¨ ¨ © § d 11 25 5 5 6 20 11 25 4 5 7 20 11 25 3 5 8 20 ) 8 ( X P = 0.3783
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Chance/Rossman, 2015 ISCAM III Example 3.1 245 Confirming our calculations using R:
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