Question

In one study of smokers who tried to quit smoking with nicotine patch​ therapy, 36 were smoking one year after treatment and 30 were not smoking one year after the treatment. Use a 0.05 significance level to test the claim that among smokers who try to quit with nicotine patch​ therapy, the majority are smoking one year after the treatment. Do these results suggest that the nicotine patch therapy is not​ effective? Identify the null and alternative hypotheses for this test.

Answer 1

The null hypothesis is that the majority of smokers who try to quit with nicotine patch therapy will still be smoking one year after treatment. The alternative hypothesis is that the majority of smokers who try to quit with nicotine patch therapy will not be smoking one year after treatment. We can use a chi-square test to determine if there is enough evidence to support the claim that nicotine patch therapy is effective in reducing smoking after one year.

Step-by-step explanation:

The null hypothesis for this test is that the majority of smokers who try to quit with nicotine patch therapy will still be smoking one year after treatment. The alternative hypothesis is that the majority of smokers who try to quit with nicotine patch therapy will not be smoking one year after treatment.

To test this claim, we can use a chi-square test. We compare the observed frequencies (36 smoking, 30 not smoking) to the expected frequencies assuming the null hypothesis is true. If the p-value is less than 0.05, we can reject the null hypothesis and conclude that the nicotine patch therapy is not effective in reducing smoking after one year.

Answer 2

In order to test the claim that the majority of smokers who try to quit with nicotine patch therapy are smoking one year after treatment, a hypothesis test can be used.

Step-by-step explanation:

In order to assess the assertion that the majority of smokers attempting to quit with nicotine patch therapy are still smoking one year post-treatment, a hypothesis test is employed.

The null hypothesis (H0) posits that the majority continue smoking one year after treatment, while the alternative hypothesis (Ha) contends that the majority do not.

Employing a significance level of 0.05, the aim is to evaluate whether the evidence suggests ineffectiveness in nicotine patch therapy.

The hypothesis test involves calculating a test statistic and comparing it to the critical value from the chi-square distribution.

If the test statistic falls within the critical region, the null hypothesis is rejected, indicating that nicotine patch therapy is not effective.

Conversely, if the test statistic does not fall within the critical region, the null hypothesis is retained, and effectiveness cannot be refuted.

This approach helps determine the efficacy of nicotine patch therapy in facilitating smoking cessation.