invest_3ed.pdf

# L use the one proportion inference applet to simulate

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(l) Use the One Proportion Inference applet to simulate these 16 infants making this helper/hinderer choice, still assuming the null model that infants have no real preference and so are equally likely to choose either toy. x Keep the Probability of heads set to 0.5. x Set the Number of Tosses to 16. x Keep the Number of repetitions at 1 for now. x Press Draw Samples . Report the number of heads (i.e., the number of infants who choose the helper toy) for this “could have been” (under the null model) outcome . (m) Uncheck the Animate box and press Draw Samples four more times, each time recording the number of the 16 infants who choose the helper toy. Did you get the same number of heads all five times? (n) Now change the Number of repetitions to 995 and press Draw Samples , to produce a total of 1000 repetitions of this null process of tossing a coin 16 times. Comment on the “null distribution of the number of infants who choose the helper toy, across these 1000 repetitions. In particular, comment on where this distribution is centered, on how spread out or variable it is (e.g., min and max values or standard deviation ), and on the distribution’s general shape. Center: Variability: Shape: Measuring “ Rareness As in Investigation A, we want a method for measuring how unusual our observation (in this case 14) is in the distribution (in this case the null distribution). We could just see whether P(X = 14) is small. But if we increase the sample size (e.g., 160 infants), than any one particular outcome will have a small probability. So we want to judge how extreme the observation is relative to the other observations in the distribution. One way to do this is to count how many observations are even more extreme. For example, if we tell you that only 1% of rattlesnakes are longer than 2.5 meters, then you know to be very surprised to see a 3 meter rattlesnake and you may even begin to think that what you are looking at is not a rattlesnake at all! Such a judgement works for any distribution and does not depend on knowing specific characteristics like the mean and standard deviation in order to be meaningful.

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Chance/Rossman, 2015 ISCAM III Investigation 1.1 24 (o) Report how many and what proportion of these 1000 samples produced 14 or more infants choosing the helper toy: x Enter 14 in the As extreme as box Number of repetitions: x Press the Count button. Proportion of repetitions: (p) Did everyone in your class get the same proportion? Does this surprise you? (q) Based on the proportion you found in (o), would you say that the actual result obtained by the researchers is very rare, somewhat rare, or not very rare, under the null model that infants have no preference and so choose blindly? Circle one of these three: Very rare Somewhat rare Not very rare (r) So, based on your simulation results, would you say that the researchers have very strong evidence that these infants’ selection process is not like flipping a coin, and instead the more plausible explanation is that these infants do have a preference for the helper toy?
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