Answer:
<em>The calculated value Z = 3.99 </em>
<em>The calculated value Z = 3.99 > 1.645 at 10% level of significance</em>
<em>Alternative hypothesis is Accepted</em>
<em>There is a difference between in the given two proportions. </em>
Step-by-step explanation:
<u>Step(i)</u>:-
Given data random survey of 500 doctors that practice specialized medicine.
First sample size 'n₁' = 500
Given data 20% felt that the government should control health care.
The first sample proportion p₁ = 20% =0.20
Given data a random sample of 800 doctors that were general practitioners
second sample size 'n₂' = 800
given data 30% felt that the government should control health care
The second sample proportion p₂ = 30% =0.30
<u><em>Step(ii)</em></u>:-
<u><em>Null hypothesis</em></u>:- H₀: There is no significant difference between the Proportions.
<u><em>Alternative hypothesis</em></u>:- H₁: There is significant difference between the Proportions.
<u><em>Test statistic</em></u>
![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-p_%7B2%7D%20%20%7D%7B%5Csqrt%7BPQ%28%5Cfrac%7B1%7D%7Bn_%7B1%7D%20%7D%20%7D%2B%5Cfrac%7B1%7D%7Bn_%7B2%7D%20%7D%20%29%20%7D)
<u><em>Where P </em></u>
<em> </em>![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%2B%20n_%7B2%7D%20p_%7B2%7D%20%20%7D%7Bn_%7B1%7D%20%2B%20n_%7B2%7D%20%7D)
<em> </em>![P = \frac{500X0.20 + 800X0.30 }{500+800 }](https://tex.z-dn.net/?f=P%20%3D%20%5Cfrac%7B500X0.20%20%2B%20800X0.30%20%7D%7B500%2B800%20%7D)
<em> P = 0.2615</em>
<em>Q = 1-P = 1- 0.2615 = 0.7385</em>
<em>Now </em>
<u><em>Test statistic</em></u>
![Z = \frac{0.20-0.30 }{\sqrt{(0.2615X0.7385)(\frac{1}{500} }+\frac{1}{800 } ) }](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7B0.20-0.30%20%7D%7B%5Csqrt%7B%280.2615X0.7385%29%28%5Cfrac%7B1%7D%7B500%7D%20%7D%2B%5Cfrac%7B1%7D%7B800%20%7D%20%29%20%7D)
<u><em>On calculation we get</em></u>
<em> </em>![Z = \frac{-0.10}{\sqrt{0.000627} }](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7B-0.10%7D%7B%5Csqrt%7B0.000627%7D%20%7D)
<em>|Z| = | -3.99|</em>
<em>The calculated value Z = 3.99 </em>
<em>The tabulated value </em>
<em> </em>
<em></em>
<u><em>Conclusion</em></u><em>:-</em>
<em>The calculated value Z = 3.99 > 1.645 at 10% level of significance</em>
<em>Null hypothesis is rejected</em>
<em>Alternative hypothesis is Accepted</em>
<em>There is a difference between in the given two proportions. </em>