To find the p-value for the test, we first need to understand that the p-value represents the probability of obtaining a test statistic at least as extreme as the one calculated, assuming the null hypothesis is true.

Step 1: Calculate the t-Statistic

We already calculated the t-statistic in the previous step:

$t \approx -0.387$

Step 2: Find the p-Value

Given that the t-statistic is $-0.387$ and the degrees of freedom (df) is $99$, the p-value can be found using a t-distribution table or statistical software.

The p-value is the area under the t-distribution curve to the left of the calculated t-value (since this is a left-tailed test).

Using a t-distribution calculator or software, the p-value corresponding to a t-statistic of $-0.387$ with $99$ degrees of freedom is approximately:

$\text{p-value} \approx 0.350$

Step 3: Interpretation

Since the p-value ($0.350$) is much larger than the significance level ($\alpha = 0.05$), we fail to reject the null hypothesis.

Conclusion: The p-value indicates that there is a 35% chance of observing a t-statistic as extreme as $-0.387$ (or more extreme) if the true mean time of car ownership is 6.5 years. This p-value is not small enough to reject the null hypothesis, confirming that we do not have enough evidence to support the claim that the mean time of car ownership is less than 6.5 years.

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Would you like to explore more details or have any questions? Here are some related questions that might interest you:

1. What does a p-value represent in the context of hypothesis testing?
2. How can you calculate p-values using statistical software or a calculator?
3. What is the difference between a one-tailed and a two-tailed p-value?
4. How does the choice of significance level affect the outcome of a hypothesis test?
5. What are Type I and Type II errors in hypothesis testing?

Tip: Understanding the p-value is crucial for interpreting the results of a hypothesis test. It helps you assess the strength of the evidence against the null hypothesis.