Question

In: Statistics and Probability

A researcher conducted an experiment in which two independent random samples of students were asked to...

A researcher conducted an experiment in which two independent random samples of students were asked to rate on a 7-point scale whether they thought animal research is wrong with 7 indicating it was wrong and 1 indicating it was not wrong. The sample sizes, means, and variances are shown separately for males and females in Table below.

Groups N Mean Variance
Females (Group 1) 17 5.353 2.743
Males (Group 2) 32 3.882 2.985

What is the correct calculated value for this test?

What is the correct critical value for this test?

Solutions

Expert Solution

For sample 1 :  
x̅1 =   5.353
s12=   2.743
n1 =   17
For sample 2 :  
x̅2 =   3.882
s22 =   2.935
n2 =    32

Null and Alternative hypothesis:              
Ho : µ1 = µ2        
H1 : µ1 ≠ µ2        
              
Pooled variance :              
S²p = ((n1-1)*s1² + (n2-1)*s2² )/(n1+n2-2)              
=   2.9026   
Test statistic:              
t = (x̅1 - x̅2) / [√(s²p(1/n1 + 1/n2 )]              
=    2.8769          
              
df = n1+n2-2          
=   47          
              
Critical value :              
At α = 0.05   and df =   47   , two tailed critical value, t crit = T.INV.2T(0.02 , 47) = ± 2.012


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