To determine which hypothesis test procedure needs to be used

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:

 

H_o    s_{1 =} s₂   no difference in variance

 

Alternate hypothesis:

 

H_o   s_{1 ≠} s₂     two tail test

 

Level of significance

0.10

 

Calculation:

 

S_{1 =}  n1 s1 / n1 -1 =  75 x 2050/ 74 =  2077.7

 

S_{2  =} 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.