Questions: Ho: μautomatic = μmanual Ha: μautomatic > μmanual Ho: μautomatic = μmanual Ha: μautomatic < μmanual Ho: μautomatic = μmanual Ha: μautomatic ≠ μmanual The test statistic is: -3.30 The p-value is: (please round to four decimal places)

Solution Steps

To solve this problem, we need to calculate the p-value for the given test statistic and then interpret the result in the context of the problem. The test statistic is -3.30, and we need to determine the p-value for this statistic under the null hypothesis. We will use a t-distribution to find the p-value and then interpret the result based on the p-value.

Given the test statistic \( t = -3.30 \), we calculate the p-value using the cumulative distribution function (CDF) of the t-distribution. For a two-tailed test, the p-value is given by:

\[ p\text{-value} = 2 \cdot P(T \leq -3.30) \]

Assuming degrees of freedom \( df = 29 \), we find:

\[ p\text{-value} \approx 0.0026 \]

The significance level commonly used is \( \alpha = 0.05 \). Since the calculated p-value \( 0.0026 < 0.05 \), we reject the null hypothesis \( H_0: \mu_{\text{automatic}} = \mu_{\text{manual}} \).

The rejection of the null hypothesis indicates that there is sufficient evidence to suggest a difference in average fuel efficiency between manual and automatic cars. Therefore, we conclude:

\[ \text{The data provide sufficient evidence that there is a difference between the average fuel efficiency of manual and automatic cars in terms of their average city mileage.} \]

Final Answer