Question

56 randomly selected male students at a commuter college were asked if they lived with their parents. 24 responded yes.   51 randomly selected female students at the same college were asked if they lived with their parents. 21 responded yes. The Dean of Students believes that more male students than female students live independently of their parents. Test the dean’s assumption. Use α=.05

1. Pooled sample proportion & compute the test statistic (Population 1 is Males, Population 2 is females)

     where

2. Critical value method, then draw the graph and mark the critical region and the test statistic.

3. P-value method, then compute the area to the right of the test statistic to get the P-value =

4. Compare to α=.05 and make a decision to reject or fail to reject the null hypothesis.

Answer 1

Sample 1:

n1 = 56

lived independently, x1 = 56-24 = 32

p̂1 = x1/n1 = 0.5714

Sample 2:

n2 = 51

lived independently, x2 = 51-21 = 30

p̂2 = x2/n2 = 0.5882

α = 0.05

a)

Null and Alternative hypothesis:

Ho : p1 = p2

H1 : p1 > p2

Pooled proportion:

p̄ = (x1+x2)/(n1+n2) = (32+30)/(56+51) = 0.579439

Test statistic:

z = (p̂1 - p̂2)/√ [p̄*(1-p̄)*(1/n1+1/n2)] = (0.5714 - 0.5882)/√[0.5794*0.4206*(1/56+1/51)] = -0.1759

b)

Critical value :

Right tailed critical value, z crit = ABS(NORM.S.INV(0.05) = 1.645

Reject Ho if z > 1.645

c)

p-value :

p-value = 1- NORM.S.DIST(-0.1759, 1) = 0.5698

d)

Decision:

p-value > α, Do not reject the null hypothesis

Conclusion:

There is not enough evidence to conclude that more male students than female students live independently of their parents.