The results of a recent study regarding smoking and two type

The results of a recent study regarding smoking and two types of illness are shown in the following table:

Illness

Non-Smokers

Smokers

Totals

Heart problem

68

82

150

Cancer

32

18

50

Totals

100

100

200

We are interested in determining whether or not Type of Illness is independent of Smoking/No-Smoking

What is the alternative hypothesis ?

Type of Illness is not independent of Smoking/Non-Smoking

Type of Illness is independent of Smoking/Non-Smoking

Type of Illness and Smoking are independent

Illness causes smoking

What is the value of the test statistic?

5.2266

10.5163

1.3079

3.0624

The p-value of the test is

between 0.025 and 0.01

more than 0.05

less than 0.01

between 0.05 and 0.025

Solution

a)

Type of Illness is not independent of Smoking/Non-Smoking [ANSWER, ALTERNATIVE HYPOTHESIS]

*********************

b)

Doing an Expected Value Chart,          
          
75   75  
25   25  
          
Using chi^2 = Sum[(O - E)^2/E],          
          
chi^2 =    5.226666667   [ANSWER, TEST STATISTIC]

*******************************  
          
With df = (a - 1)(b - 1), where a and b are the number of categories of each variable,          
          
a =    2      
b =    2      
          
df =    1      
          
          
Thus, the p value is, using table,          
          
[BETWEEN 0.025 AND 0.01, OPTION A]