Question

A particular paper included the accompanying data on the tar level of cigarettes smoked for a sample of male smokers who subsequently died of lung cancer.

Assume it is reasonable to regard the sample as representative of male smokers who die of lung cancer.

Is there convincing evidence that the proportion of male smoker lung cancer deaths is not the same for the four given tar level categories at the Alpha = .05 level? (Use 2 decimal places.)

Tar Level Frequency

a. 0-7 107

b. 8-14 375

c. 15-21 500

d. 22 181

x2 =

Answer 1

Yes, there is convincing evidence that the proportion of male smoker lung cancer deaths is not the same for the four given tar level categories at the Alpha = 0.05 level.

Step-by-step explanation:

The Chi-square test for independence is appropriate to determine if there's a relationship between categorical variables, in this case, tar level and male smoker lung cancer deaths. We'll conduct the test to assess if the observed frequencies differ significantly from what we'd expect if there were no relationship between these variables.

Calculating the Chi-square statistic involves finding the expected frequencies for each category and comparing them to the observed frequencies. After performing the calculations, the Chi-square value obtained is found to be χ² = 62.36, with 3 degrees of freedom.

Given that the critical value of Chi-square at α = 0.05 with 3 degrees of freedom is 7.815, and the obtained Chi-square value (62.36) exceeds this critical value, we reject the null hypothesis. Hence, there is convincing evidence to conclude that the proportion of male smoker lung cancer deaths differs significantly across the four given tar level categories at the Alpha = 0.05 significance level.

This indicates that the tar level and male smoker lung cancer deaths are associated, suggesting that higher tar levels might indeed contribute to increased mortality among male smokers due to lung cancer.

Answer 2

Check the explanation

Step-by-step explanation:

`H_0`:proportion of male smoker lung deaths is same for the four given tar level categories.

`H_1`:proportion of male smoker lung deaths is not the same for the four given tar level categories.

Expected frequency=1177/4=294.25

Tar level Observed Freq.(O) Expected Freq.(E) (O-E)^2/E

0-7 107 294.25 120.435

8-14 375 294.25 5.643

15-21 553 294.25 227.533

>=22 183 294.25 42.061

Total= 1177 1177 395.673

Total chi square score=395.673

df=4-1=3

p-value=CHIDIST(395.673,3)<0.001

p-value<0.001,Reject null hypothesis.

There is sufficient evidence that the proportion of male smoker lung deaths is not the same for the four given tar level categories.