Null Hypothesis: The proportion of male independents are equal to the proportion

Question

Null Hypothesis: The proportion of male independents are equal to the proportion of female independents.

                Alternative Hypothesis: The proportion of male independents are not equal to the proportion of female independents.

                12/28 female independents

                16/28 male independents

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.

g) Summarize the results i.e. give the best answer to the question in (a).

h) Report the p-value together with its definition.

Explanation / Answer

a) Is proportion of male independents eqaul to proportion of female independents.

b) H0: Pu1=Pu2 (Proportion of female independents are eqaul to proportion of male independents)

c) alpha=0.05.

d) Z critical=+-1.96

e) Pu=(n1ps1+n2ps2)/(n1+n2)=(28*12/28+28*16/28)/(28+28)=0.5

SigmaP-P=sqrt[Pu(1-Pu)]sqrt[(n1+n2)/n1*n2]

=sqrt[0.5*0.5]sqrt[(28+28)/28*28]=0.13

Z=(ps1-ps2)-(pu1-pu2)/SigmaP-P

=(12/28-16/28)-0/0.13

=-1.10

f) Reject H0, if test statistic falls in critical region.

g) Here, test statistic do not fall in critical region. Failure to reject H0. Insufficient sample evidence to conclud etht a proportion of female independet are not equal to proportion of male independents.

h) p value:0.271332, p valu ei snot less than alpha=0.05, failure to reject H0.

h)

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