MATH 2830 Final Project Name: Section: 005 INSTRUCTIONS: 1. Identify a group of three people [or more if you like!] for your project (if you like the team work. Otherwise, you may do it by yourself). In the case of a team work, each person will be responsible for an equal portion of the project. 2. The answers [to the questions asked] should be clearly in a steplike arrangement and typed. 3. Your final work should be submitted [to me, in my office] by the Final exam date . 4. There's no Project Presentation. . Page 1 of 2 Please go on to the next page. . . 1. A thumbtack that is tossed on a desk can land in one of the two ways shown in the following illustration: Brad and Dan cannot agree on the likelihood of obtaining a head or a tail. Brad argues that obtaining a tail is more likely than obtaining a head because of the shape of the tack. If the tack had no point at all, it would resemble a coin that has the same probability of coming up heads or tails when tossed. But the longer the point, the less likely it is that the tack will stand up on its head when tossed. Dan believes that as the tack lands tails, the point causes the tack to jump around and come to rest in the heads position. Brad and Dan need you to settle their dispute. Do you think the tack is equally likely to land heads or tails? To investigate this question, find an ordinary thumbtack and toss it a large number of times (say, 100 times). (a) What is the meaning, in words, of the unknown parameter in this problem? (b) Set up the null and alternative hypotheses and compute the p-value based on your results from tossing the tack. (c) How would you answer the original question now? If you decide the tack is not fair, do you side with Brad or Dan? (d) What would you estimate the value of the parameter in part (a) to be? Find a 90% confidence interval for this parameter. (e) After doing this experiment, do you think 100 tosses are enough to infer the nature of your tack? Using your result as a preliminary estimate, determine how many tosses would be necessary to be 95% certain of having 4% accuracy; that is, the margin of error of estimate is 4%. Have you observed enough tosses? Page 2 of 2 End of exam