Question

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 t-test for these means

b) Find the effect size

Answer 1

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 = (x1-x2)/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,

P-value is = 2*0.0143 = 0.0286

As the obtained, p-value is < 0.05.

We reject the null hypothesis Ho.

B)

Effect size = (x1-x2)/pooled s.d

Pooled s.d =

Sp = √{(n1-1)*s1^2 + (n2-1)*s2^2 }/√{n1+n2-2}

After substitution,

Effect size = −0.0976104890 = -0.0976