Question

1. Minorities in Higher Education

You are a social psychologist interested in the adjustment of international students who go to school at American universities. You decide to examine whether there are differences in scores on the Acceptability by Others Scale (AOS). The AOS is a scale that ranges from 1 to 20 (1 = feeling completely isolated – 20 feeling completely accepted) that measures acceptance within the college community. You collect scores on the AOS from a sample of international students (Int) at a small college in the United States and another sample of United States (U.S.) citizens attending the same college. The data is provided below. Conduct a two-tailed independent-samples t-test by hand using an alpha level of .05 to determine whether there are differences in AOS scores between the two samples. Record your answers below.

International Students	U.S. Students
10	17
10	13
9	19
18	10
6	14
4	16
4	20
9	20
20	13
20	19

1. Step #1: A priori expectations
   1. Question of interest:

2. Prediction:

2. Step #2: Set up hypotheses
   1. H₀:

2. H₁:

3. Step #3: Set criteria for decision
   1. t_cv (critical value for rejecting the null hypothesis)

2. Decision rule for when to reject the null hypothesis:

4. Step #4: Collect data/ compute statistic

							M =
							μ =
							df =
							sM =
							t =
							d =

5. 
   Step #5: Report results in standard format – Must include test statistic , degrees of freedom, p-value , 95% confidence interval (95% C.I.) and conclusion (reject or fail to reject H₀)

​​​​​​​6. Step #6: Interpret the results of the statistical test in terms of the research question

Answer 1

Hypothesis test:

Data:        

n1 = 10       

n2 = 10       

x1-bar = 11       

x2-bar = 16.1       

s1 = 6.1824       

s2 = 3.4785       

Hypotheses:        

Ho: μ1 = μ2        

Ha: μ1 ≠ μ2        

Decision Rule:        

α = 0.05       

Degrees of freedom = 10 + 10 - 2 = 18      

Lower Critical t- score = -2.100922037       

Upper Critical t- score = 2.100922037       

Reject Ho if |t| > 2.100922037       

Test Statistic:        

Pooled SD, s = √[{(n1 - 1) s1^2 + (n2 - 1) s2^2} / (n1 + n2 - 2)] =   √(((10 - 1) * 6.1824^2 + (10 - 1) * 3.4785^2)/(10 + 10 -2)) =     5.016

SE = s * √{(1 /n1) + (1 /n2)} = 5.01607575750207 * √((1/10) + (1/10)) = 2.243257275      

t = (x1-bar -x2-bar)/SE = -2.273479755       

p- value = 0.035478669       

Decision (in terms of the hypotheses):        

Since 2.273479755 > 2.100922037 we reject Ho    

Conclusion (in terms of the problem):        

There is sufficient evidence that there are differences in AOS scores between the two samples

Confidence interval:

n1 = 10

n2 = 10

x1-bar = 11

x2-bar = 16.1

s1 = 6.1824

s2 = 3.4785

% = 95

Degrees of freedom = n1 + n2 - 2 = 10 + 10 -2 = 18

Pooled s = √(((n1 - 1) * s1^2 + (n2 - 1) * s2^2)/DOF) = √(((10 - 1) * 6.1824^2 + ( 10 - 1) * 3.4785^2)/(10 + 10 -2)) = 5.016075758

SE = Pooled s * √((1/n1) + (1/n2)) = 5.01607575750207 * √((1/10) + (1/10)) = 2.243257275

t- score = 2.100922037

Width of the confidence interval = t * SE = 2.10092203686118 * 2.24325727481268 = 4.712908643

Lower Limit of the confidence interval = (x1-bar - x2-bar) - width = -5.1 - 4.71290864300311 = -9.812908643

Upper Limit of the confidence interval = (x1-bar - x2-bar) + width = -5.1 + 4.71290864300311 = -0.387091357

The 95% confidence interval is [-9.813, -0.387]