I need to create three questions with this information with hypothesis testing s

Question

I need to create three questions with this information with hypothesis testing step by step

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Explanation / Answer

Solution:

Required three questions for hypothesis testing are given as below:

Whether the proportion of women with political affiliation as democrat is same as the proportion of men with political affiliation as democrat?

Whether the proportion of men with political affiliation as democrat is same as the proportion of men with political affiliation as republican?

Whether the proportion of green eye women is same as that of men?

Hypothesis testing for the first question is given as below:

Whether the proportion of women with political affiliation as democrat is same as the proportion of women with political affiliation as republican?

Here, we have to use two sample z test for the population proportion.

The null and alternative hypotheses for this test are given as below:

Null hypothesis: H0: The proportion of women with political affiliation as democrat is same as the proportion of women with political affiliation as republican.

Alternative hypothesis: Ha: The proportion of women with political affiliation as democrat is not same as the proportion of men with political affiliation as democrat.

H0: p1 = p2 versus Ha: p1 p2

This is a two tailed test.

We consider a level of significance or alpha value as 5%. ( = 0.05)

We are given

X1 = Number of women with political affiliation as democrat = 5

N1 = total number of women = 23

X2 = Number of men with political affiliation as democrat = 2

N2 = total number of men = 29

P1 = X1/N1 = 5/23 = 0.217391

P2= X2/N2 = 2/29 = 0.068966

Test statistic formula is given as below:

Z = (P1 – P2) / sqrt[(P1*(1 – P1)/N1)+(P2*(1 – P2)/N2)]

Z = (0.217391 - 0.068966) / sqrt((0.217391*(1 - 0.217391)/23)+( 0.068966*(1 - 0.068966)/29))

Z = 1.513975

Lower critical value = -1.96

Upper critical value = 1.96

P-value = 0.1194

(P-value and critical values are calculated by using z-table or excel)

P-value > = 0.05

So, we do not reject the null hypothesis that the proportion of women with political affiliation as democrat is same as the proportion of women with political affiliation as republican.

There is sufficient evidence to conclude that the proportion of women with political affiliation as democrat is same as the proportion of women with political affiliation as republican.

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