Question

A telephone poll of 750 adults was taken. The question asked was: “Should the federal tax on cigarettes be raised to pay for health care reform?” Of the 502 nonsmokers, 300 said yes. Of the 248 smokers, 50 said yes. At á = 0.05, test the claim that the proportion of nonsmokers in favor of the federal tax is greater than the proportion of smokers in favor of the tax.

Answer 1

Given that,

For Non-smokers : n1 = 502, x1 = 300 and

For Smokers : n2 = 248, x2 = 50 and

The null and alternative hypotheses are,

H0 : p1 = p2

Ha : p1 > p2

This test is right-tailed test.

Pooled proportion is,

Test statistic is,

=> Test statistic = Z = 10.23

p-value = P(Z > 10.23) = 0.0000

Since, p-value is less than a = 0.05, we reject the null hypothesis.

Therefore, there is sufficient evidence to support the claim that the proportion of nonsmokers in favor of the federal tax is greater than the proportion of smokers in favor of the tax.

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