Question

question 6
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.
the health official surveys 200 randomly selected 12th graders and finds that 14 of them have used tobacco in the past 30 days.
h₀: the percentage of 12th graders who have smoked in the past 30 days is equal to 8.4%.
h₁: 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. reject h₀.
b. accept h₀.
c. fail to reject h₀.

Explanation:

Step1: Recall decision - rule for hypothesis testing

In hypothesis testing at a significance level $\alpha$, if the p - value is greater than $\alpha$, we fail to reject the null hypothesis $H_0$. If the p - value is less than or equal to $\alpha$, we reject $H_0$. Here, the significance level $\alpha = 0.05$ and the p - value is $0.09$.

Step2: Compare p - value and significance level

Since $0.09>0.05$ (p - value > $\alpha$).

Answer:

C. Fail to reject $H_0$