Question

A simple random sample of 800 individuals provides 100 Yes responses. a. What is the point estimate of the proportion of the population that would provide Yes responses (to 2 decimals)? b. What is your estimate of the standard error of the proportion (to 4 decimals)? c. Compute the 95% confidence interval for the population proportion (to 4 decimals). ( , )

Answer 1

Answer: a) 0.13

b)
`(0.1067,\ 0.1533)`

Explanation:

The confidence interval for population proportion is given by :-

`p\pm z_(\alpha/2)\sqrt{(p(1-p))/(n)}`

Given : Sample size : n= 800

Number of individuals provides Yes responses = 100

a) The proportion of individuals provides Yes responses =
`p=(100)/(800)=0.125\approx0.13`

hence, the the point estimate of the proportion of the population that would provide Yes responses :
`p=0.13`

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

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

Now, the 90% two-sided confidence interval on the proportion of people who regularly have a dental checkup will be :-

`0.13\pm (1.96)\sqrt{(0.13(1-0.13))/(800)}\\\\\approx0.13\pm0.0233\\\\=(0.13-0.0233,0.13+0.0233)\\\\=(0.1067,\ 0.1533)`