In a study, researcher wishes to study whether there is significance difference

Question

In a study, researcher wishes to study whether there is significance difference in the percentage of smokers between male and female population. The data in the contingency table below. In a random sample of subjects. 20 of them were male smokers. 40 were male non-smokers. 12 of them were female smokers and 60 were female non-smokers. State null and alternative hypotheses perform this test at 5% level of significance by reporting the value of the test statistic reporting the p-value for the test, and then write a conclusion (Please use p-value approach to answer this question. Do not need to show the detail computations.)

Explanation / Answer

a) Ho: smoking is independent of gender

Ha: Smoking is not independent of Gender

b) TEst statistics = sum (Oi-Ei)^2/Ei = 4.95

c) df = (r-1)(c-1) = 1

p-value = 0.026090

d) since p-value < alpha(0.05)

we reject the null hypothesis and conclude that

there is signiifcant evidence thta both are dependent

c1 c2 total r1 20 40 60 r2 12 60 72 total 32 100 132 Oi 20 40 12 60 Ei 14.54545 45.45455 17.45455 54.54545 sum (Oi-Ei)^2/Ei 2.045455 0.654545 1.704545 0.545455 4.95 critical value 3.84 p-value 0.026090668

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