invest_3ed.pdf

# S n x enter a large number for number of samples x

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S = n = x Enter a large number for Number of samples x Press Draw Samples x For Number of successes , enter 80 but toggle the button to change the > to < x Check Two-sided x Check Exact Binomial

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Chance/Rossman, 2015 ISCAM III Investigation 1.4 47 The applet found a p-value by adding two tail probabilities together; what were the cut-off values for these tails? How do the cut-offs compare to what you anticipated above? What value does it report for the exact two-sided p-value? (i) What conclusion do you draw from this p-value about whether the probability of a kissing couple leaning to the right is 0.74? Explain briefly. Strong evidence against the null hypothesis? Why are you making this decision? (j) Dr. Güntürkün actually conjectured 2/3 as the process probability of a kissing couple leaning to the right (consistent with some other right-sided tendencies by humans). Repeat (h) to determine a two- sided p-value for testing this hypothesis. Report the p-value and summarize your conclusion about the plausibility that S = 2/3. [ Hint : In R, use iscambinomtest , with alternative=“two.sided” (in quotes, with the period).] (k) Repeat your analysis method from (j) to determine whether 0.60 is a plausible value for the probability that a kissing couple leans to the right. Study Conclusions These sample data provide strong evidence against the null hypothesis that kissing couples lean to the right 74% of the time (two-sided p-value = 0.0185), but we are not able to reject the null hypothesis that the probability of turning to the right in this kissing process is equal to 2/3 (two-sided p-value = 0.6341) or 0.60 (p-value = 0.3151). It is plausible that this sample result (80 successes out of 124 trials) came from a process where the probability of success for the process was 2/3. But it is also plausible that the sample result came from a process where the probability of success was 0.60. Note that we haven’t proven either of these values to be the correct one. The sample data allow for many (technically, infinitely many) plausible values of this probability, as you will explore in the next investigation. We should be cautious in generalizing these results to all kissing couples. Based on the study description, the researcher did attempt to get a broad representation of couples, but there could be some hidden sources of bias.
Chance/Rossman, 2015 ISCAM III Investigation 1.4 48 (l) Return to the case where S = 0.74. We found the cut-offs for the two-sided p-value to be 80 (our observed result) and 104 (as being just as extreme on the other side of the expected value). Use 104 as the observed count in the applet. What value does the applet use for the lower cut-off, still 80? Technical Details In calculating a two-sided p-value in the previous investigation, we considered the values that were as extreme as 80 “or more extreme” which we interpreted to be “as far from the expected value.” When S = 2/3, the expected number of successes out of 124 is 82.67 so that the observed value of 80 successes in the sample is 2.67 below this expected value. We can also find P( X < 80) to be 0.336 using the binomial distribution.

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