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Step 4: Draw Inferences. 12. Is the sample proportion who associated âTimâ with the face on the left greater than the probability specified in the null hypothesis? 13. Is it possible that the sample proportion could turn out to be this large even if the null hypothesis were true? As we did with Buzz and Doris in Section 1.1, we will use simulation to investigate how surprising the observed sample result would be, if in fact subjects were just as likely to associate âTimâ with the face on the left as they were to associate âBobâ with the face on the left. (Note also that our null model assumes the same probability for all subjects.) 14. We will now use the One Proportion applet to conduct this simulation analysis. a. First enter the probability of success value specified in the null hypothesis. b. Enter the appropriate sample size (number of subjects in this study). c. Enter 1 for the number of samples, and press Draw Samples. Report the number of âsuccessesâ in this simulated sample. d. Now, select the radio button for âProportion of successes.â Report the proportion of successes in this simulated sample. Use your answer to âcâ to verify how this value is calculated. e. Leaving the âProportion of successesâ radio button selected, click on Draw Samples four more times. Do you get the same results each time? f. Now enter 995 for the number of samples and click on Draw Samples, bringing the number of simulated samples to 1000. Comment on the center, variability, and shape of the resulting distribution of sample proportions. This distribution of simulated sample proportions is called the null distribution, because it is based on assuming the null hypothesis to be true. 15. Restate the observed value of the sample proportion, pÌ , who associated âTimâ with the face on the left. June 27, 2014 MAA PREP workshop 21