For these exercises, perform each of these steps. Assume that all variables are normally or approximately normally distributed.
a. State the hypotheses and identify the claim.
b. Find the critical value(s).
c. Compute the test value.
d. Make the decision.
e. Summarize the results.
Use the traditional method of hypothesis testing unless otherwise specified and assume the variances are unequal.

The out-of-state tuitions (in dollars) for random samples of both public and private four-year colleges in a New England state are listed. Find the 95% confidence interval for the difference in the means.

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Private 13,600 13,495 16,590 17,300 23,400 12,500 Public 7,050 9,000 6,450 9,758 7,050 7,871 16,100