The Donner Party: Natural Selection in Action The Donner Partyis the name of emigrants who travelled in covered wagons fromIllinois to California in 1846 and became trapped in the SierraNevada Mountains when the region was hit by heavy snows in lateOctober. By the time the survivors were rescued in April, 1847, 40out of 87 had died from famine and exposure to severe cold. Some ofthose that survived did so by resorting to cannibalism, accordingto newspapers reporting at that time. Data on the survivorship ofthe party members may be used to gain some insight into humanbehavior and natural selection under extreme stress. For example,some questions of interest are whether males are better able towithstand harsh conditions than females and the extent to which thechances of survival vary with age. The data in the lab assignmentcome from Grayson, (1990), “Donner Party Deaths: A DemographicAssessment,” Journal of Anthropological Research, v.46. The dataare also available in the StatCrunch file lab3.txt located on theSTAT 151 Laboratories web site athttp://www.stat.ualberta.ca/statslabs/stat151/index.htm (click Stat151 link, and Data for Lab 3). The data are not to be printed inyour submission. The following is a description of the variables inthe data file: Variable Name Description of Variable NAME full nameof the passenger, GENDER gender (female or male); FAMILY familyname, POSITION member status within the family, AGE estimated age(in years) as of July 31, 1846; CHILD child (yes or no) SURVIVALsurvived or died, ORDER order of death, ALONE Yes if travellingalone (no family, no close accompanying persons), GROUP SIZE Numberof group members. 1. Is it an observational study or a randomizedexperiment? Can the data be generalized to a broader population? Iffemales in the study turned out to be more apt to survive thanmales, could this be used as proof that, in general, females arebetter able than males to withstand harsh conditions? 4. In thisquestion, you will examine the relationship between survival andgender. (a) Were the chances of survival different for females thanfor males? In order to answer the question, obtain the contingencytable of survival by gender. Make sure that Row percent, Columnpercent, and Percent of Total as well as Chi-Square test forindependence are selected. Paste the table into your report. (b)Using α = 0.05, test that there was no relationship betweensurvival and gender. State the null and alternative hypotheses.Report the value of the appropriate test statistic, thedistribution of the test statistic under the null hypothesis, andthe P-value of the test to answer the question. State yourconclusion. (c) Refer to the output in part (a) to answer thefollowing questions: What percent of the survivors were females?What percent were female survivors? (d) Using α = 0.05, is thereevidence that there was a difference in the survival rate forfemales and males? Carry out the appropriate two-sample proportiontest. State the null and alternative hypotheses. Report the valueof the appropriate test statistic, the distribution of the teststatistic under the null hypothesis, and the P-value of the test toanswer the question. State your conclusion. (e) What is therelationship between the tests in parts (b) and (d)? 3 (f) Obtainand interpret a 95% confidence interval for the difference insurvival rates of females and males?