Question

In a random survey of 500 doctors that practice specialized medicine, 20% felt that the government should control health care. In a random sample of 800 doctors that were general practitioners, 30% felt that the government should control health care. Test the claim that there is a difference in the proportions. Use a = 0.10

Answer 1

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

$Z = \frac{p_{1}-p_{2} }{\sqrt{PQ(\frac{1}{n_{1} } }+\frac{1}{n_{2} } ) }$

Where  P

   $P = \frac{n_{1}p_{1} + n_{2} p_{2} }{n_{1} + n_{2} }$

   $P = \frac{500X0.20 + 800X0.30 }{500+800 }$

  P  = 0.2615

Q = 1-P = 1- 0.2615 = 0.7385

Now

Test statistic

$Z = \frac{0.20-0.30 }{\sqrt{(0.2615X0.7385)(\frac{1}{500} }+\frac{1}{800 } ) }$

On calculation we get

 $Z = \frac{-0.10}{\sqrt{0.000627} }$

|Z| = | -3.99|

The calculated value  Z  = 3.99

The tabulated value

 $Z\frac{\alpha }{2} = Z\frac{0.10}{2} = Z_{0.05} = 1.645$

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.