Question

Two different simple random samples are drawn from two different populations. The first sample consists of 20 people with 9 having a common attribute. The second sample consists of 2100 people with 1492 of them having the same common attribute. Compare the results from a hypothesis test of p 1equalsp 2 ​(with a 0.05 significance​ level) and a 95​% confidence interval estimate of p 1minusp 2.

Answer 1

Answer:
`(-0.48,\ -0.04)`

Explanation:

The confidence interval for the difference of two population proportion is given by :-

`(p_1-p_2)\pm z_(\alpha/2)\sqrt{(p_1(1-p_1))/(n_1)+(p_2(1-p_2))/(n_2)}`

Given : The first sample consists of 20 people with 9 having a common attribute.

Here,
`n_1=20` ,
`p_1=(9)/(20)=0.45`

`n_2=2100` ,
`p_1=(1492 )/(2100)\approx0.71`

Significance level :
`\alpha=1-0.95=0.05`

Critical value :
`z_(\alpha/2)=1.96`

A 95% confidence interval for the difference of two population proportion will be :-

`(0.45-0.71)\pm z_(\alpha/2)\sqrt{(0.45(1-0.45))/(20)+(0.71(1-0.71))/(2100)}\\\\\approx -0.26\pm0.22\\\\=(-0.26-0.22,-0.26+0.22)\\\\=(-0.48,\ -0.04)`