What hypothesis testing procedure should you use to answer these questions? Assume all samples are simple random samples, and assume α = 0.05 if it isn’t specified.
A state-by-state survey found that the proportion of adults who are smokers in Alabama and Missouri was 24.7% and 28.7%, respectively. Each has a sample size of 2000. At α = 0.01, can you support the claim that the proportion of smokers is lower in Alabama than in Missouri?
To answer this question, you would use a hypothesis testing procedure known as a two-sample proportion test. The null hypothesis (H0) would be that the proportion of smokers in Alabama is the same as the proportion of smokers in Missouri. The alternative hypothesis (Ha) would be that the proportion of smokers in Alabama is lower than the proportion of smokers in Missouri.
H0: p1 = p2
Ha: p1 < p2
Here, p1 represents the proportion of smokers in Alabama, and p2 represents the proportion of smokers in Missouri.
To perform the test, you would calculate the test statistic using the formula:
test statistic = (p1 - p2) / sqrt(p(1-p)(1/n1 + 1/n2))
Where p represents the pooled proportion, which is calculated as (x1+x2) / (n1+n2), x is the number of successes (smokers) in each sample, and n is the sample size.
Once you have the test statistic, you would compare it to the critical value from the standard normal distribution (z-score) at the chosen significance level (α = 0.01 in this case). If the test statistic is less than the critical value, you would reject the null hypothesis and conclude that the proportion of smokers is lower in Alabama than in Missouri.
Note: To calculate the test statistic and perform the hypothesis test, you would need the actual number of smokers in each state, not just the proportions.