Answer:
Test statistic Z= 0.13008 < 1.96 at 0.10 level of significance
null hypothesis is accepted
There is no difference proportion of positive tests among men is different from the proportion of positive tests among women
Step-by-step explanation:
Step(I):-
Given surveyed two random samples of 390 men and 360 women who were tested
first sample proportion
[tex]p_{1} = \frac{360}{390} = 0.9230[/tex]
second sample proportion
[tex]p_{2} = \frac{47}{52} = 0.9038[/tex]
Step(ii):-
Null hypothesis : H₀ : There is no difference proportion of positive tests among men is different from the proportion of positive tests among women
Alternative Hypothesis:-
There is difference between proportion of positive tests among men is different from the proportion of positive tests among women
[tex]Z = \frac{p_{1}- p_{2} }{\sqrt{PQ(\frac{1}{n_{1} }+\frac{1}{n_{2} } } }[/tex]
where
[tex]P = \frac{n_{1}p_{1} +n_{2} p_{2} }{n_{1}+n_{2} }[/tex]
P = 0.920
[tex]Z= \frac{0.9230-0.9038}{\sqrt{0.920 X0.08(\frac{1}{390}+\frac{1}{52} } )}[/tex]
Test statistic Z = 0.13008
Level of significance = 0.10
The critical value Z₀.₁₀ = 1.645
Test statistic Z=0.13008 < 1.645 at 0.1 level of significance
Null hypothesis is accepted
There is no difference proportion of positive tests among men is different from the proportion of positive tests among women