1. To determine which hypothesis test procedure needs to be used
particulars Undergraduate debt
Private college Public college
Size 75 205
Mean 28100 22000
Standard deviation 2050 2084

 

The  t-test  should  be  the  optimum  choice  because  it  will determine  the  result  by  two independent samples of two population  means. If you want to check whether the variance is equal or not, then two-sample variance test can be applied.

 

Solution:

 

N1 = 75 n2 = 205     x1 = 28100 x2 = 2200 s1 = 2050 s2 = 2084

 

Null hypothesis:

 

Ho    s1 = s2   no difference in variance

 

Alternate hypothesis:

 

Ho   s1 ≠ s2     two tail test

 

Level of significance

0.10

 

Calculation:

 

S1 =  n1 s1 / n1 -1 =  75 x 2050/ 74 =  2077.7

 

S2  = n2 s2 / n2 -1  = 205 x 2084/204 = 2094.2

 

Then:

2077.7 / 2094.2 = 0.992

 

  1. Indicate the appropriate test that should be used to determine if a difference exists

 

T-test is the test that can be used if a difference is present. But if a difference is not present then two tail tests should be done.