The long string of short paragraphs is the transcript of the info. If answering a question is not possible for any reason, skipping it is fine just whatever is possible to be answered with the given info. Also, on question number 5, two blanks have been filled in ignore the answers there and, if possible, give the correct one. Thanks You!
Background Information and Initial Thoughts Do babies prefer a nice person over a mean person? This researcher decided to study that. She showed babies a "helper" and a "hinderer\" in action. Then she asked the babies to choose the character they wanted to play with. She recorded that 14 of the 16 babies chose the "helper.\" \"There's a domain of developmental psychololgy called theory of mind which involves basically asking how do we develop an understanding of other minds, how do we come to understand other people's thoughts their relationship between their thoughts, and their behaviors if you don't want to do different things what could you do how we reason about other minds in the world. It began addressing some of these questions with infants in this study parents bring their six month olds into the lab. At the other side of a long table is a hill stage. A red circle with googly eyes tries to climb the hill, he sort of goes up the hill and then falls back down, he always fails at it and a blue square character also with googly eyes comes from the bottom of the hill and bumps him up to the top of the hill. So that he isn't successful on different trials, the climber tries again to get to the top of the hill and then a yellow triangle character comes down from the top and bumps him to the bottom of the hill to prevent him from getting his goal. The baby(s) see this a number of times until they get nice and bored with it. Then they do a choice measure where moms are asked to close their eyes, an experimenter who did not see on which character was which brings over the two characters to the babies and just sees which character the baby touches rst. We found that impressively, actually almost a hundred percent of babies preferred the more positive character(The blue square). Thus, they seem to have attraction to helpful prosocial individuals and also a real aversion to antisocial unhelpful individuals. Babies are fascinated by the social world. Young babies are all about entering the social world, making connections with different social individuals, looking at the interconnections between different social individuals, and guring out what that means. So I think these studies very nicely show how babies are evaluating individuals out in the world and how babies themselves are developing attitudes and towards different individuals.\" What is the sample and population for the experiment? What are the statistic and parameter? Since % of the babies selected the Helper toy it appears that the babies / are not (choose one) randomly choosing a toy. I believe that they can/cannot (choose one) distinguish between the Helper and the Hinderer toys. Simulation 4. One problem with number3 is that maybe 14 out of 16 isn't really that unusual even if the babies cannot distinguish between the two toys. We need to repeat the experiment many times in order to see how often 14 (or more) out of 16 babies choose the Helper. This is obviously not possible for us or practical for the researchers. We need to simulate many experiments. If babies are just randomly picking a character, then they would have a 50% chance of picking the helper. This is the same chance as getting Heads when you ip a coin. Simulate the experiment using coins. Flip 16 coins for each simulation and record whether it comes up Heads or Tails. We will let Heads mean that the baby chose the \"helper\" and Tails mean that they baby chose the \"hinderer.\" Simulation 1: _h_ _h_ _t_ _t_ _h_ _t_ _t_ _t_ _h_ _h_ _h_ _t_ _t_ _h_ t h Simulation 2: _h_ _h_ _h_ _t_ _h_ _h_ _t_ _t_ _h_ _t_ _h_ _h_ _h_ _t_ h h Find the number of the simulated babies who selected the Helper character. Simulation 1: number selected = proportion = Simulation 2: number selected = proportion = Describe process: Probability of heads: 0.5 Number of tosses: 16 Number of All Attempts(Last Repetition) repetitions: 10000 Animate Draw Samples Total = 200000 Heads(Last Repetition) = 7 FOR QUESTION Choose statistic: NUMBER 5 o Number of heads Proportion of heads Tails(Last Repetition) = 9 As extreme as 2 14 Summary Stats Count Mean = 8.001 0.0021 Proportion of repetitions: SD = 2.001 415 / 200000 = 0.0021 10000 20000 30000 4000 Options: O Two-sided Exact Binomial Normal Approximation O 2 4 6 8 10 12 14 16 | 2 14 Number of heads Reset Show previous Show sliders5. Our work so far is pretty inadequate to answer number 6. What we need is hundreds or thousands of simulated samples of 16 babies, but this would take too long. So we have an applet that can do this for us. Go to httgzlz www.rossmanchance.com[appletleneProgZOneProp.htm. On the applet, we will leave the probability of Heads at .5, but we will change the number of tosses to 16. We can put in however many repetitions we would like, but if you are doing more than 1, please turn off \"Animate" or you will be there for a long time. Once you are ready, select \"Draw Samples." Every time you click on this button, it will do the number of repetitions you have selected and add the results to what you had previously. Do at least 5,000 repetitions total. (I've done 10,000 at a time all the way up to 200,000.) In the "As extreme as" box, you can put in 14, since that's the number we saw happen. The applet will count the number of samples where Heads came up 14 or more times and calculate the chance of that happening. List your results below. Number with 14 or more Heads: Total number of repetitions: 250,000 % with 14 or more Heads: 0.002196 Note: This number would be an estimate of our p-value and represents the chance that we could see 14 out of 16 babies choose the helper if they are just guessing. Conclusion 6. Assuming that the babies are randomly picking a toy, how likely does it appear to be that 14 or more babies out of 16 would choose the helper toy? Explain by considering how many of our simulations produced 14, 15, or 16 simulated babies that picked the helper toy
