Answer:
a) The point estimate of the difference between the populations is Md=-0.14.
b) The margin of error at 95% confidence is 0.212.
c) The 95% confidence interval for the difference between means is (-0.352, 0.072).
Explanation:
We have to calculate a 95% confidence interval for the difference between means.
The sample 1 (ships under 500 passengers), of size n1=20 has a mean of 6.93 and a standard deviation of 0.31.
The sample 2 (ships over 500 passengers), of size n2=55 has a mean of 7.07 and a standard deviation of 0.6.
The difference between sample means is Md=-0.14.

The estimated standard error of the difference between means is computed using the formula:

The critical t-value for a 95% confidence interval is t=1.993.
The margin of error (MOE) can be calculated as:

Then, the lower and upper bounds of the confidence interval are:
The 95% confidence interval for the difference between means is (-0.352, 0.072).