Two random samples are taken from private and public universities (out-of-state tuition) around the nation. The yearly tuition is recorded from each sample and the results can be found below. Test to see if the mean out-of-state tuition for private institutions is statistically significantly higher than public institutions. Assume unequal variances. Use a 1% level of significance.

Private Institutions (Group 1 )	Public Institutions (Group 2)
43,120	25,469
28,190	19,450
34,490	18,347
20,893	28,560
42,984	32,592
34,750	21,871
44,897	24,120
32,198	27,450
18,432	29,100
33,981	21,870
29,498	22,650
31,980	29,143
22,764	25,379
54,190	23,450
37,756	23,871
30,129	28,745
33,980	30,120
47,909	21,190
32,200	21,540
38,120	26,346

Hypotheses:

H₀: ₁(?) ₂

H₁: ₁ (?) ₂

What are the correct hypotheses for this problem?