4.
Group Statistics 

protestant 
N 
Mean 
Std. Deviation 
Std. Error Mean 

HIGHEST YEAR OF SCHOOL COMPLETED 
.00 
1260 
13.32 
3.219 
.091 
1.00 
745 
13.62 
2.810 
.103 
Using this information
a) Conduct an independent samples ttest for these means
b) Find the effect size
A)
Answer)
As the sample sizes are extremely large, we can use standard normal z table to estimate the answer.
Null hypothesis Ho : u1 = u2
Alternate hypothesis Ha : u1 not equal to u2
Test statistics z = (x1x2)/standard error
Standard error = √{(s1^2/n1)+(s2^2/n2)}
X1 = 13.32, X2 = 13.62
N1 = 1260, N2 = 745
S1 = 3.219, S2 = 2.81
After substitution,=
Z = 2.19
From z table, P(z<2.19) = 0.0143
As the test is two tailed,
Pvalue is = 2*0.0143 = 0.0286
As the obtained, pvalue is < 0.05.
We reject the null hypothesis Ho.
B)
Effect size = (x1x2)/pooled s.d
Pooled s.d =
Sp = √{(n11)*s1^2 + (n21)*s2^2 }/√{n1+n22}
After substitution,
Effect size = −0.0976104890 = 0.0976
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