Respuesta :
Answer:
The calculated value Z = 3.99
The calculated value Z = 3.99 > 1.645 at 10% level of significance
Alternative hypothesis is Accepted
There is a difference between in the given two proportions.
Step-by-step explanation:
Step(i):-
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
Step(ii):-
Null hypothesis:- H₀: There is no significant difference between the Proportions.
Alternative hypothesis:- H₁: There is significant difference between the Proportions.
Test statistic
[tex]Z = \frac{p_{1}-p_{2} }{\sqrt{PQ(\frac{1}{n_{1} } }+\frac{1}{n_{2} } ) }[/tex]
Where P
[tex]P = \frac{n_{1}p_{1} + n_{2} p_{2} }{n_{1} + n_{2} }[/tex]
[tex]P = \frac{500X0.20 + 800X0.30 }{500+800 }[/tex]
P = 0.2615
Q = 1-P = 1- 0.2615 = 0.7385
Now
Test statistic
[tex]Z = \frac{0.20-0.30 }{\sqrt{(0.2615X0.7385)(\frac{1}{500} }+\frac{1}{800 } ) }[/tex]
On calculation we get
[tex]Z = \frac{-0.10}{\sqrt{0.000627} }[/tex]
|Z| = | -3.99|
The calculated value Z = 3.99
The tabulated value
[tex]Z\frac{\alpha }{2} = Z\frac{0.10}{2} = Z_{0.05} = 1.645[/tex]
Conclusion:-
The calculated value Z = 3.99 > 1.645 at 10% level of significance
Null hypothesis is rejected
Alternative hypothesis is Accepted
There is a difference between in the given two proportions.
