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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%.Ha: 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? Reject H0. Accept H0. Fail to reject H0.

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.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%.Ha: 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? Reject H0. Accept H0. Fail to reject H0.

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Solution

The correct conclusion is "Fail to reject H0". The p-value of 0.09 is greater than the significance level of 0.05. This means that there is not enough evidence to reject the null hypothesis (H0) that the percentage of 12th graders who have smoked in the past 30 days is equal to 8.4%. Therefore, we cannot conclude that there has been a statistically significant decrease in teen smoking rates.

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