Question

3.

Group Statistics
	newengland	N	Mean	Std. Deviation	Std. Error Mean
HIGHEST YEAR OF SCHOOL COMPLETED	.00	1937	13.38	3.073	.070
	1.00	81	14.72	2.955	.328

a) Conduct an independent samples t-test for these means

Answer 1

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 = 13.38, X2 = 14.72

N1 = 1937, N2 = 81

S1 = 3.073, S2 = 2.955

After substitution,=

Z = -3.99

From z table, P(z<-3.99) = 0

As the test is two tailed,

P-value is = 2*0 = 0

As the obtained, p-value is < 0.05.

We reject the null hypothesis Ho.