Question

a government health official is interested in whether there has been a statistically significant decrease in teen smoking rates. in 2013, 8.4 percent of 12th graders had used tobacco in the past 30 days. with this data, we test the following hypotheses at the 5% significance level.
$h_0$: the percentage of 12th graders who have smoked in the past 30 days is equal to 8.4%.
$h_1$: the percentage of 12th graders who have smoked in the past 30 days is greater than 8.4%.
the p - value is 0.09. which conclusion is correct?
a. fail to reject $h_0$.
b. accept $h_0$.
c. reject $h_0$.

Explanation:

Step1: Recall the decision rule

In hypothesis testing, if the p - value \(> \alpha\) (significance level), we fail to reject the null hypothesis \( H_0 \).

Step2: Identify the values

Here, the significance level \(\alpha = 0.05\) (5% significance level) and the p - value \(= 0.09\).

Step3: Compare p - value and \(\alpha\)

Since \(0.09>0.05\) (i.e., p - value \(>\alpha\)), we fail to reject \( H_0 \).

Answer:

A. Fail to reject \( H_0 \).