Q3 (10 pts) In Lab9, you watcheda video about the Simpson's Paradox. The video has the following narration: "....One study in the UK appeared to show that smokers had a higher survival rate than nonsmokers over a twenty-year period. That is, until dividing the participants by age group showed that the nonsmokers were significantly older on average, and thus, more likely to die during the trial period, precisely because they were living longer in general. Here, the age groups are the lurking variable and are vital to correctly interpret the data...."

The video was most likely referring to the surveys carried out in Whickham, a small town in northeast England. The survey was conducted in 1972-1974 and collected the respondents' age and smoking status. Twenty years later, a follow-up was conducted to determine whether the respondents were still alive. We will focus on a subset of the original sample: women who were either current smokers or had never smoked at the time of the first survey.

Among a total of 1314 women, 582 were smokers. After the 20-year period, 443 smokers and 502 non-smokers were alive.

1. (2 pts) Complete the following contingency table by filling in the blanks (the shaded area in the table). There is no need to explain.

	Alive (during follow-up)	Dead (during follow-up)	Total
Smokers
Non-smokers
Total

1. (2 pts) Compute the risk of death for the smoker group and the risk of death for the non-smoker group. Which group has a higher risk of death? Please show your work.Hint: you should find that the nonsmokers have a higher risk of death.

In Part (c)-(d), we will consider a third variable (called a "lurking variable" in the video): the age group. The women were put in three age groups: 18-54, 55-64, and 65-84.

1. (2 pts) Complete the table below by filling in the blanks (the shaded area in the table). You can use the values already given in the table and the information given in the beginning of the Q3, such as "443 smokers and 502 non-smokers were alive.

	Age group: 18-54	Age group: 55-64	Age group: 65-84
	Alive	Dead	Total	Alive	Dead	Total	Alive	Dead	Total
Smokers	373	43	380 416	64	52	116	(1)		50
Non- smokers	393	24	417	81	41	122	28		193

Please explain how you obtain the value for Blank (1). There is no need to explain how you got the values for the other two blanks.Hint: You should get 6 for Blank (1).

1. (3 pts) Based on the Table in Part (c), compute the risk of death for smokers and the risk of death for non-smokers for each of the three age groups. Fill in the blanks (the shaded area in the table below) with the computed risks.

	Risk of death
	Risk of death in age group 18-54	Risk of death in age group 55-64	Risk of death in age group 65-84
Smokers	(2)
Non-smokers

Please show your work for Blank (2). There is no need to show work for the other blanks.Hint: You should get 0.103 for Blank (2).

1. (1 pt) Explain how Simpson's Paradox takes place in this study.