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 and round answers to 4 decimal places.

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

Identify the test statistic. Round to 4 decimal places.