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

Answer:

$\boxed{\boxed{0.218\ and\ 0.382}}$

Step-by-step 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,

$M.E=Z_{critical}\cdot \sqrt{\dfrac{p(1-p)}{n}$

Putting all the values,

$M.E=1.96\times \sqrt{\dfrac{0.3(1-0.3)}{121}}=0.082$

Hence, the interval will be,

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

$=0.3\pm 0.082$

$=0.218,0.382$