Question

A study was conducted in China concerning smoking versus lung cancer. It was found that of the 226 people that did smoke, 126 of them contracted lung cancer. Of the 96 people that did not smoke, 35 of them contracted lung cancer. Does the data suggest that smoking increases the incidence of lung cancer? Address this question using proportions and an odds ratio. Which technique do you think best presents the results? Why?

Answer 1

Solution:

Here, we have to use two sample z test for population proportions.

Null hypothesis: H₀: Smoking does not increase the incidence of lung cancer.

Alternative hypothesis: H_a: Smoking increases the incidence of lung cancer.

H₀: p₁ = p₂ versus H_a: p₁ > p₂

This is an upper tailed (one tailed) test.

We are given X1=126, N1=226, X2=35, N2=96

We assume α = 0.05

Test statistic for z test for two population proportions is given as below:

Z = (P1 – P2) / sqrt(P*(1 – P)*((1/N1) + (1/N2)))

Where,

P = (X1+X2)/(N1+N2) = (126 + 35) / (226 + 96) = 0.50

P1 = X1/N1 = 126/226 = 0.557522124

P2 = X2/N2 = 35/96 = 0.364583333

Z = (0.557522124 - 0.364583333) / sqrt(0.50*(1 – 0.50)*((1/226)+(1/96)))

Z = 3.1675

P-value = 0.0008

(by using z-table)

P-value < α = 0.05

So, we reject the null hypothesis

There is sufficient evidence to conclude that Smoking increases the incidence of lung cancer.