The manufacturer claims that your new car gets $31 \mathrm{mpg}$ on the highway. You suspect that the mpg is less for your car. The 54 trips on the highway that you took averaged $29.4 \mathrm{mpg}$ and the standard deviation for these 54 trips was $9 \mathrm{mpg}$. What can be concluded at the $\alpha=0.01$ level of significance? a. For this study, we should use t-test for a population mean b. The null and alternative hypotheses would be: $0^{8}$ $0^{\circ}$ $\sigma^{4}$ $\infty^{s}$ $\infty^{\circ}$ $\sigma^{s}$ c. The test statistic $t \hat{\div}^{2}=$ (please show your answer to 3 decimal places.) d. The $p$-value $=$ (Please show your answer to 4 decimal places.) e. The $p$-value is $\alpha$ f. Based on this, we should fail to reject the null hypothesis. $0^{\circ}$

Step 1 ：Define the null hypothesis as the mean mpg of the car being 31, and the alternative hypothesis as the mean mpg being less than 31.

Step 2 ：Given the sample mean (29.4), the sample standard deviation (9), and the sample size (54), calculate the t statistic and the p-value.

Step 3 ：Calculate the t statistic using the formula \(t = \frac{{\bar{x} - \mu}}{{s/\sqrt{n}}}\), where \(\bar{x}\) is the sample mean, \(\mu\) is the population mean, s is the sample standard deviation, and n is the sample size. The calculated t statistic is approximately -1.306.

Step 4 ：Calculate the p-value using a t-distribution table or a statistical software. The calculated p-value is approximately 0.099.

Step 5 ：Compare the p-value with the significance level (0.01). Since the p-value is greater than the significance level, fail to reject the null hypothesis.

Step 6 ：Conclude that there is not enough evidence to support the claim that the mean mpg of the car is less than 31.

Step 7 ：Final Answer: \(\boxed{\text{Fail to reject the null hypothesis}}\)