A transportation analyst claims that the average commute time in a major city is less than $45$ minutes. A hypothesis test is conducted, with a resulting P-value of $0.0084$. What would be the conclusion at a significance level $\alpha =.01$

• A. We reject $H_0$ because we have enough evidence that the average commute time is less than $45$ minutes
• B. We adopt $H_0$ because we lack sufficient evidence that the average commute time is less than $45$ minutes
• C. No conclusion can be made

Answer: (A)

Verified step by step guidance

1. Identify the null hypothesis (H0) and the alternative hypothesis (H1). In this case, H0: The average commute time is 45 minutes or more, and H1: The average commute time is less than 45 minutes.
2. Determine the significance level (α), which is given as 0.01.
3. Compare the P-value (0.0084) to the significance level (α = 0.01).
4. If the P-value is less than the significance level, reject the null hypothesis (H0). If the P-value is greater than or equal to the significance level, do not reject the null hypothesis.
5. Since the P-value (0.0084) is less than the significance level (0.01), we reject the null hypothesis (H0) and conclude that there is enough evidence to support the claim that the average commute time is less than 45 minutes.