Answer:
|Z| = |-4.089| > 1.645 at 0.10 level of significance
Null hypothesis is rejected at 0.10 level of significance
<em>There is a difference between the two Population proportions</em>
Step-by-step explanation:
<u><em>Step(i)</em></u>:-
Given first sample size (n₁) = 50
Given proportion of the first sample p⁻₁= 0.2
Given second sample size (n₂) = 50
Given proportion of the second sample p₂⁻ = 30/50 = 0.6
<em>Null Hypothesis : H₀: p₁⁻=p₂⁻</em>
<em>Alternative Hypothesis : H₁: p₁⁻≠p₂⁻</em>
<u><em>Step(ii):-</em></u>
Z-statistic
![Z = \frac{p_{1} -p_{2} }{\sqrt{pq(\frac{1}{n_{1} } +\frac{1}{n_{2}) } } }](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7Bp_%7B1%7D%20-p_%7B2%7D%20%7D%7B%5Csqrt%7Bpq%28%5Cfrac%7B1%7D%7Bn_%7B1%7D%20%7D%20%2B%5Cfrac%7B1%7D%7Bn_%7B2%7D%29%20%7D%20%7D%20%7D)
Where
![P = \frac{n_{1}p_{1} +n_{2} p_{2} }{n_{1} +n_{2} }](https://tex.z-dn.net/?f=P%20%3D%20%5Cfrac%7Bn_%7B1%7Dp_%7B1%7D%20%2Bn_%7B2%7D%20%20p_%7B2%7D%20%7D%7Bn_%7B1%7D%20%2Bn_%7B2%7D%20%7D)
![P = \frac{50X0.2+50X0.6}{50+50} = 0.4](https://tex.z-dn.net/?f=P%20%3D%20%5Cfrac%7B50X0.2%2B50X0.6%7D%7B50%2B50%7D%20%3D%200.4)
<em>Z-statistic</em>
![Z = \frac{0.2-0.6}{\sqrt{0.4 X 0.6(\frac{1}{50}+\frac{1}{50} } }](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7B0.2-0.6%7D%7B%5Csqrt%7B0.4%20X%200.6%28%5Cfrac%7B1%7D%7B50%7D%2B%5Cfrac%7B1%7D%7B50%7D%20%20%7D%20%7D)
Z = -4.089
Level of significance =0.10
Z₀.₁₀ = 1.645
|Z| = |-4.089| > 1.645 at 0.10 level of significance
Null hypothesis is rejected at 0.10 level of significance
<u><em>Final answer</em></u>:-
<em>There is a difference between the two Population proportions</em>