Show all your work Indicate clearly the methods you use, because you will be scored on the conrectness of your methads as well as on the accuracy and completeness of your! (results and explanations. Afair die with its faces numbered from 1 to 6, is one in which each number is equallylkely to land face up when the die is rolled On a fairdie, the probability that the number 6 will land face upts A group of students wanted to nvestigate a claim aboutmanipualing a fair die so that It favors one outoome, The claim stales thatif a far die Is pul Into an oven and baked at 200 F for 10mnutes, the Inside of the die willbegin to melt, When the die cools the inside will be sold again, but with more weighttoward the botom, This shift in weight will couse the face that was up when the die.cooled to land up more often that the other faces The students obtained a fair die and baked it ac and the numbet 6 landed faceup 43 times. Letprepresent the popularion proportion of times the number 6 will land face upon the baked dietthe die could be rolled an infinile mumberof times, rding to the preceding directions. The die cooled with the number 6 face up. After the die cooled, they rolled the die 200 timec (a) Clarke, one of the students, constructed a f5 percent confidence interval for pas 0,215 +0.057. Does the interval provide convincing statistical evidence that the number 6 will land face up more often ofi the baked die than on a fair de? Explan your reasoning. (b) Aurelia, another student, suggested they conduct a signficance test to investigate the claim She tested the hypotheses Hn p- vensus H. sp - ar the significance evel of n (1.05 She obtained a test etatistic of 1.83 with a prvalue of 0.0033.Do the resulte of the significancetest agree with the results of Clarkes confidence interval in part (a)7 Explain your reasoning, (e) Two standard normal.curves are shown below, one forthe confidence interval calculateed in part (al and one forthe aionificance testopnducted in part (b). 0 For the confidence intervalcurve, label the critical values for the 95% confidence level and shace the area that rebresents va ues in the cuter5 O For the significance test curve, label the critical value for the 5%% significance level and shade the area representing the values of a that would lead to a rejection of the null hypothesis in pert (b), Confidence Interval Hypothesis Test ()Joachim, a third student, noted that the confidence inlerval in pert (ek glves plausble values ol the porameter as an interval between two values. Hle suggeated that they develop a one-sided confidence interval because they were on y conceined with whether the number 6 was landing face up more often than expected not less often. The one sided-inlerval will delermine a value L such that all plausible values of pare greater than . The formula forZ is L-61etv Delermine the values of z needed to create the onesided 95 peroent confidence interval. Then caculate the value of . Do the results of Joachim's one-sided confidence interva. agree wth results.of Aurelia's signficance test in part (b) Explain your reasoning.