Question

Use the Chi-square test for independence to test the null hypothesis of no association between cigarette smoking and asthma symptoms. The expected cell counts, have been computed for you.

Ever Smoked Cigarettes (OBSERVED)
Symptoms of Asthma	Yes	No	Total
Yes	20	30	50
No	22	78	100
Total	42	108	150

Ever Smoked Cigarettes (EXPECTED)
Symptoms of Asthma	Yes	No	Total
Yes	14	36	50
No	28	72	100
Total	42	108	150

4) (10 points) Conduct the test at a significance level of 0.05 and in your analysis include -the null and alternative hypotheses,
-the degrees of freedom,
-the test statistic,

-the p-value
-and the conclusion of the test.

Answer 1

(1)

Ho: The two variables cigarette smoking and asthma symptoms are independent.

Ha: The two variables cigarette smoking and asthma symptoms are not independent.

(2) df = (2-1) * (2-1) = 1

(3) Test statistics:

Squared distances	Yes	No	Total
Yes	2.571	1.000	3.571
No	1.286	0.500	1.786
Total	3.857	1.500	5.357

= 5.357

(4) p value = 0.02064

(5) As the p value (0.02064) is less than (0.05) we reject the Null hypothesis.

Hence we have sufficient evidence to believe that cigarette smoking and asthma symptoms are not independent.