# Team Bayes: MATH 6630: FPP Exercise SET A P. 18 ex. 4,6

[p: 18 question 4] No. In fact, there were many new recruits to the program at the beginning of the second year, and these people turned out to have been in worse shape than those who entered at the beginning of the first year.

The tests at the end of the first year showed a considerable improvement in the physical fitness of the participants. However, comparing the results at the end of the second year with the beginning of the first year, the phyisical fitness seem to have deteriorated. Those results doesn't show that the second year of the program was a failure, because it might be that the participants were very excited about the program in the first year that they achieved good fitness results , but in the second year they were less enthusiastic and they stopped following the program as seriously. moreover they might have changed their eating habits in the second year which may affect their fitness level making it worse than the beginning of the first year. also, the recruits of the first might have been very fit people and responded really well to the program which induced a great response in the second year i.e. new recruits joined the program and they might not be in as good shape as the people in the first year therefore the results in the second year turned out to be worse than the beginning of the first year. In other words, in this kind of experiment we have to be very careful about confounding variables, that may affect our conclusion. One possible solution is to take two randomly selected groups at the beginning of the second year from the participants of the first year. One group should be the control group which doesn't follow the program in the second year, and the second group is the treatment group that sticks to the program in the second year. By comparing the results for both groups we can have more accurate conclusions.

[pp:18 question 6]

To decide whether three out of 24,000 is a lot ar a little, we have to compare it to something. Out of 24000 persons only three persons died, this is a very small proportion of the whole population and cannot prove that the vaccine failed to protect against the virus. this experiment is poorly designed because it is observational and doesn't allow us to compare a control group with a treatment group to test whether the vaccine have significant effects. this observational experiment could be biased against the vaccine, the 3 people who died might have severe medical conditions that made them vulnerable to the virus that even a vaccination couldnt save them. in this experiment a lot of confounding variables were not controlled for. for example the three deceased individuals might be living in very unsanitary neighborhoods and their immunity system is very weak and can't respond to the vaccination. Moreover those 3 people might have gotten the virus even before they were administered the vaccine which makes the experiment biased against the vaccine.