Dally Driving The average number of miles a person drives per day is 24 . A researcher wishes to see if people over age 60 drive less than 24 miles per day. She selects a random sample of 40 drivers over the age of 60 and finds that the mean number of miles driven is 22.7 . The population standard deviation is 2.9 miles. At $\alpha=0.01$, is there sufficient evidence that those drivers over 60 years old drive less than 24 milies per day on average? Assume that the variable is normally distributed. Use the P-value method with a graphing calculator. Part: $0 / 4$ Part 1 of 4 (a) State the hypotheses and identify the claim. \[ \begin{array}{l} H_{0}=\square \text { (Choose one) } \mathbf{\nabla} \\ H_{1}=\square \text { (Choose one) } \mathbf{V} \end{array} \] This hypothesis test is a (Choose one) $\mathbf{v}$ test.
Solution
Step 1 ：State the hypotheses and identify the claim.
Step 2 ：The null hypothesis (H0) is typically a statement of no effect or no difference. The alternative hypothesis (H1) is what you might believe to be true or hope to prove true.
Step 3 ：In this case, the researcher is testing whether people over age 60 drive less than 24 miles per day. So, the null hypothesis would be that people over age 60 drive 24 miles per day (i.e., there is no difference from the average), and the alternative hypothesis would be that people over age 60 drive less than 24 miles per day.
Step 4 ：This is a one-tailed test because we are only interested in whether people over age 60 drive less than 24 miles per day, not whether they drive more.
Step 5 ：Final Answer: \[\boxed{\begin{array}{l} H_{0}: \mu = 24 \\ H_{1}: \mu < 24 \end{array}}\] This hypothesis test is a one-tailed test.
