Question

A random sample of 121 observations produced a sample proportion of 0.3. An approximate 95% confidence interval for the population proportion p is between

a) 0.258 and 0.342

b) 0.202 and 0.398

c) 0.218 and 0.369

d) 0.231 and 0.369

e) 0.218 and 0.382

Please show work for rating

Answer 1

`\boxed{\boxed{0.218\ and\ 0.382}}`

Explanation:

A random sample of 121 observations produced a sample proportion of 0.3

Here,

1. 
   `p=0.3`
2. 
   `n=121`

`Z_(critical)` for a 95% confidence level = 1.96

So the interval will be,

`=p\pm \text{Marginal Error}`

Marginal Error can be calculated as,

`M.E=Z_(critical)\cdot \sqrt{(p(1-p))/(n)`

Putting all the values,

`M.E=1.96* \sqrt{(0.3(1-0.3))/(121)}=0.082`

Hence, the interval will be,

`=p\pm \text{M.E}`

`=0.3\pm 0.082`

`=0.218,0.382`