Question

A research article described a random sample of 584 smokers who tried to quit smoking by using either a nicotine patch or e-cigarettes (fake cigarettes producing nicotine in water vapor form). After six months, 7.3 percent of those using e-cigarettes had stopped smoking, compared with 5.8 percent of those wearing the patch. To see if quitting result is significantly associated with the method used, which of the following statistical inference procedure should we use?

A. Matched pairs t test
B. Two-sample t test
C. Chi-square test for goodness of fit
D. Chi-square test for two-way table

Answer 1

D. Chi-square test for two-way table

Explanation:

To test if there is an association between the percentage of people that successfully stop smoking and the method they used to do so, a random sample of 584 smokers who tried to quit smoking and was orted by the method they used to help themselves to achieve their goal (nicotine-patch or e-cigarettes). After six months, the proportion of subjects that successfully stopped smoking.

In this case, the t-test is not applicable, this statistic is to test the population mean. The variable of the study is the proportion of people that successfully stopped smoking using either method.

To apply Chi-Square tests the condition to be met is that the variable is categorizable and since the data can be organized in a 2x2 table, all expected frequencies should be >5.

The objective of the Goodness-to-fit test is to test if a population follows a certain theoretical model.

In this example, the objective is to compare the proportion of people that successfully quit smoking and the proportion of people that failed by using either method.