Question

The Donner Party: Natural Selection in Action The Donner Party is the name of emigrants who travelled in covered wagons from Illinois to California in 1846 and became trapped in the Sierra Nevada Mountains when the region was hit by heavy snows in late October. By the time the survivors were rescued in April, 1847, 40 out of 87 had died from famine and exposure to severe cold. Some of those that survived did so by resorting to cannibalism, according to newspapers reporting at that time. Data on the survivorship of the party members may be used to gain some insight into human behavior and natural selection under extreme stress. For example, some questions of interest are whether males are better able to withstand harsh conditions than females and the extent to which the chances of survival vary with age. The data in the lab assignment come from Grayson, (1990), “Donner Party Deaths: A Demographic Assessment,” Journal of Anthropological Research, v.46. The data are also available in the StatCrunch file lab3.txt located on the STAT 151 Laboratories web site at http://www.stat.ualberta.ca/statslabs/stat151/index.htm (click Stat 151 link, and Data for Lab 3). The data are not to be printed in your submission. The following is a description of the variables in the data file: Variable Name Description of Variable NAME full name of the passenger, GENDER gender (female or male); FAMILY family name, POSITION member status within the family, AGE estimated age (in years) as of July 31, 1846; CHILD child (yes or no) SURVIVAL survived or died, ORDER order of death, ALONE Yes if travelling alone (no family, no close accompanying persons), GROUP SIZE Number of group members. 1. Is it an observational study or a randomized experiment? Can the data be generalized to a broader population? If females in the study turned out to be more apt to survive than males, could this be used as proof that, in general, females are better able than males to withstand harsh conditions? 4. In this question, you will examine the relationship between survival and gender. (a) Were the chances of survival different for females than for males? In order to answer the question, obtain the contingency table of survival by gender. Make sure that Row percent, Column percent, and Percent of Total as well as Chi-Square test for independence are selected. Paste the table into your report. (b) Using α = 0.05, test that there was no relationship between survival and gender. State the null and alternative hypotheses. Report the value of the appropriate test statistic, the distribution of the test statistic under the null hypothesis, and the P-value of the test to answer the question. State your conclusion. (c) Refer to the output in part (a) to answer the following questions: What percent of the survivors were females? What percent were female survivors? (d) Using α = 0.05, is there evidence that there was a difference in the survival rate for females and males? Carry out the appropriate two-sample proportion test. State the null and alternative hypotheses. Report the value of the appropriate test statistic, the distribution of the test statistic under the null hypothesis, and the P-value of the test to answer the question. State your conclusion. (e) What is the relationship between the tests in parts (b) and (d)? 3 (f) Obtain and interpret a 95% confidence interval for the difference in survival rates of females and males?

Answer 1

1.

It is an observational study as we are observing what was already there or what was already happened to draw inference unlike in randomized experiment where there is an intervention by the researchers by introducing intervention to the treatment group and control group receives placebo or receives nothing. Here, we are dealing with or studying the particular case where there is no intervention but only pure observation of the event or incident.

The data cannot be generalised to a broader population unless we assume certain things such as similar fitness and health levels, similar knowledge and similar exposure levels, etc,. And the data must be sufficiently large. 87 is a good sample. However, before we generalise it, we need to study more of such cases of various similar incidents. We even need to conduct experiments before we generalise but such cases cannot be dealt with experiments as it is about survival and we cannot play with lives of people for our study purpose - it's not possible and not recommendable, but must be condemned. So, the only way to do in order to generalise is to study more of such cases that took place across the globe or in the space. If there are no sufficient cases, we just need to wait for them to happen and then observe when they happen. However, if we have other possible and recommendable ways/methods, we can proceed with them.

So, if females are found out to be more apt to survive than males, we need to conduct the appropriate statistical tests to see if the difference is significant where we assume certain level of significance such as 5% or 1% (generally) or others. And here we only conclude saying - reject null hypothesis or fail to reject null hypothesis, but do not accept the alternative hypothesis and thus, no possibility to generalise the significant difference (where null hypothesis(H0) says that no significant difference between males and females regarding withstanding harsh conditions and alternative hypotheses (H1) is that there exists a significant difference between males and females regarding withstanding harsh conditions). And we must also see if the sample we are observing is representative of the population of interest and there are high chances that it is not so because no care is taken about sample selection as we are just observing what happened already.

Due to all these limitations and other unknown or undealt limitations, we cannot generalise our conclusions of this observational study. Studying more of such cases is necessary.