Two random samples are taken from private and public universities (out-of-state tuition) around the nation

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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 )

43,120

28,190

34,490

20,893

42,984

34,750

44,897

32,198

18,432

33,981

29,498

31,980

22,764

54,190

37,756

30,129

33,980

47,909

32,200

38,120

 

 

 

Public Institutions (Group 2)

25,469

19,450

18,347

28,560

32,592

21,871

24,120

27,450

29,100

21,870

22,650

29,143

25,379

23,450

23,871

28,745

30,120

21,190

21,540

26,346

 

 

Hypotheses:

H₀: μ₁ = μ₂

H₁: μ₁ > μ₂

Identify the test statistic. Round to 4 decimal places.

t =___