To test whether there is strong evidence of a difference between the average fuel efficiency of cars with manual and automatic transmissions in terms of city mileage, we can perform a two-sample t-test. Here's the formulation of the hypotheses:

Null Hypothesis ($H_0$):

There is no difference in the average city mileage between cars with manual and automatic transmissions. $H_0: \mu_{\text{manual}} = \mu_{\text{automatic}}$ This can also be written as: $H_0: \mu_{\text{manual}} - \mu_{\text{automatic}} = 0$

Alternative Hypothesis ($H_a$):

There is a difference in the average city mileage between cars with manual and automatic transmissions. $H_a: \mu_{\text{manual}} \neq \mu_{\text{automatic}}$

This is a two-tailed test because the alternative hypothesis does not specify the direction of the difference.

Test Conditions:

• The data comes from two independent random samples.
• The sample sizes ($n = 26$) for both groups are reasonably large, and the t-test is robust to mild deviations from normality.

Would you like me to calculate the test statistic, p-value, and conclude the test?