Question

In 2022, the cdc reported that 12.5% of u.s. adults currently smoke cigarettes. from the same report, a random sample of 12,405 ohioans was taken with 2543 being current smokers. using α = 0.05, test whether the proportion of ohioans that smoke cigarettes is different than the proportion of u.s. adults.

a. accept the null hypothesis
b. reject the null hypothesis
c. inconclusive
d. further analysis required

Answer 1

The proportion of Ohioans who smoke is statistically different from the national average of 12.5%, as indicated by a two-tailed z-test for proportion with a significance level of α = 0.05, resulting in the rejection of the null hypothesis.

Step-by-step explanation:

In testing whether the proportion of Ohioans that smoke cigarettes is different from the proportion of U.S. adults, our null hypothesis (H0) is that there is no difference in the proportions, meaning the proportion of Ohioan smokers is equal to the national average (12.5%). The alternative hypothesis (H1) is that there is a difference, meaning the proportion of Ohioan smokers is not equal to the national average.

For our sample of 12,405 Ohioans, with 2,543 being current smokers, the sample proportion is 2,543/12,405 = 0.205 or 20.5%. Using a significance level of α = 0.05, we perform a two-tailed z-test for proportion. Since the provided information indicates a decision to reject the null hypothesis was made, it suggests that the test statistic calculated had a corresponding p-value less than 0.05. Therefore, we conclude that there is sufficient statistical evidence to suggest that the proportion of Ohioans who smoke is significantly different from the national average of 12.5%.