Question

According to the U.S. Dept. of Transportation, teens ages 16-19 drive an average of 7,624 miles per year. Believing that students in rural areas drive farther to school, work, and activities than other students, one dad randomly sampled 50 high school and college students between 16 and 19 years old who live in various rural areas and found that they drove an average of 7,701 miles per year, with a standard deviation of 336 . A hypothesis test was conducted to determine if the sample provided enough evidence to support the dad's belief that teens living in rural areas drive more miles, on average, than the U.S. average for teens. The p-value for the test was 0.0558.

Select the best conclusion.
A. We reject the null, because the dad's sample provided enough evidence to conclude that the average miles per year driven by teens in rural areas is greater than the U.S. average.
B. We fail to reject the null, because the dad's sample did not provide enough evidence to conclude that the average miles per year driven by teens in rural areas is greater than the U.S. average.
C. We reject the null, because the dad's sample did not provide enough evidence to conclude that the average miles per year driven by teens in rural areas is greater than the U.S. average.
D. We fail to reject the null, because the dad's sample provided enough evidence to conclude that the average miles per year driven by teens in rural areas is greater than the U.S. average.

Answer 1

We fail to reject the null hypothesis since the p-value of 0.0558 is greater than the significance level of 0.05, indicating not enough evidence that rural teens drive more than the national average.

Step-by-step explanation:

Based on the information provided, the dad conducted a hypothesis test to determine if teens living in rural areas drive more miles than the national average for teenagers, which is 7,624 miles per year. The sample data showed an average of 7,701 miles per year with a standard deviation of 336 miles. The p-value obtained from the test was 0.0558. To make a decision about the null hypothesis, we compare the p-value to the significance level. Typically, a significance level (alpha) of 0.05 is used, meaning if the p-value is less than 0.05, we reject the null hypothesis assuming sufficient evidence against it.

Since the p-value of 0.0558 is slightly greater than the common alpha level of 0.05, we fail to reject the null hypothesis. This means that there isn't enough statistical evidence to support the claim that teenagers in rural areas drive more on average than the stated national average for teens.

Therefore, the correct conclusion is: B. We fail to reject the null, because the dad's sample did not provide enough evidence to conclude that the average miles per year driven by teens in rural areas is greater than the U.S. average.