To perform a hypothesis test, we need to identify the null hypothesis $(H_0)$ and the alternative hypothesis $(H_1)$. Given that the problem is testing whether the mean time of the taxi cab rides is less than 15 minutes, the hypotheses are stated as follows:

1. $H_0$ (Null Hypothesis): The mean time is equal to 15 minutes. This is the default claim we are challenging. $H_0: \mu = 15$

2. $H_1$ (Alternative Hypothesis): The mean time is less than 15 minutes. This is what we aim to provide evidence for. $H_1: \mu < 15$

Next Steps:

If you have a Minitab display showing the output of a hypothesis test, such as a $t$-value, $p$-value, and degrees of freedom, we would typically use the $p$-value to make a decision based on the significance level of 0.05.

1. If $p$-value < 0.05, reject $H_0$.
2. If $p$-value ≥ 0.05, fail to reject $H_0$.

Would you like a detailed interpretation using the Minitab values, or do you have any specific values from the display you'd like me to address?

Related Questions:

1. What is the critical $t$-value for a one-tailed test at the 0.05 significance level with 34 degrees of freedom?
2. How would the conclusion change if the significance level was 0.01?
3. What assumptions are necessary for the $t$-test in this scenario to be valid?
4. How do you calculate the $t$-statistic manually given sample mean, sample size, and standard deviation?
5. What other hypothesis tests could be used if the sample size or distribution assumptions were different?

Tip: In hypothesis testing, always define the null and alternative hypotheses clearly before performing any calculations. This helps maintain clarity and consistency in interpreting the results.