Question 1
[25]
South Africans has voted for jobs and against the high cost of living, power and water cuts and
high levels of crime. The cabinet must be evaluated according to how Ramaphosa responded
to these priorities. Very big, very bloated, but will the government of national unity (GNU)
cabinet be better? This is the question which was asked a group of boys and girls around
Thohoyandou. Their responses were recorded in the table below, where Y is for yes and N is
for no.
Girls
Boys
YYYYNYYNYYNYNYNNYYNNY Y Y NYYNY
YYNYNY YNYYYYYNY NYYYYNNYYNYYYN
NYNNNNYYYYYNYYNYNNNYYYYNYYYNYY
YYNNY YN YNYNYYNYNNNY Y Y Y N Y YYNYNY
If $p_1$ is the proportion of girls population who reply yes and $p_2$ is the proportion of boy
population who reply yes:
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a. Find the 95% confidence interval for the difference between the two population proportions.
[12]
b. Is there sufficient evidence at $\alpha = 0.01$, to conclude that the proportion of girls who replied
yes is more than the proportion of boys who replied yes? Use the critical value approach.
[13]
