Null Hypothesis: Proportion of women with a college degree is equal to the propo

Question

Null Hypothesis: Proportion of women with a college degree is equal to the proportion of women without a college degree.

Alternative Hypothesis: Proportion of women with a college degree is not equal to the proportion of women without a college degree.

8/23 women have college degrees 15/23 women without college degrees

a) Present the question that you are trying to answer (it should be one sentence long).

b) State your null and alternative hypothesis using mathematical symbols.

c) Select the level of significance you wish to use in your study

d) Find critical region (indicate if you are using one- or two-tailed test.

e) Calculate the test value.

f) Make the decision to reject or not to reject the null hypothesis.

Explanation / Answer

a) Is proportion of women with college degree is different from proportion of women withut college degree?

b) H0:Pu1=Pu2 (proportion of women with college degree is same as that of proportion of women without college degree)

H1:Pu1 not equal to Pu2 (proportion of women with college degree is different from proportion of women without college degree)

c) Alpha=0.05.

d) For two-tailed test, Zcritical=+1.96

e) Compute population proportion, pu=(n1ps1+n2ps2)/(n1+n2)=(23*8/23+23*15/23)/(23+23)=0.5

Sigmap-p=sqrt [pu(1-pu)]sqrt[(n1+n2)/n1*n2]=sqrt[0.5(1-0.5)]sqrt[(23+23)/23*23]=0.15

Z=(ps1-ps2)-(p1-p2)/Sigmap-p=[(8/23-15/23)-0]/0.15=-2.03

f) The test statistic falls incritical region, therefore, reject H0 to conclude that proportion of women with college degree is same as that of proportion of women without college degree.

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