Answer:
Given:
The population proportion $(p^*)=0.20$
The margin of error $(e)=0.07$
The confidence interval level $=97%$
Solution:
โ The significance level at 97% confidence interval:
$(\alpha)=1-0.97=0.03$
โ The critical value at 0.03 significance level $(z_c)=2.17$
$ \Rightarrow $ The sample size $(n):$
โ Here we need to use a margin of error formula to find out the sample size
$$ \therefore e = z_c \cdot \sqrt{\frac{p(1 – p)}{n}} \quad $$ $$ \therefore 0.07 = 2.17 \cdot \sqrt{\frac{0.20(1 – 0.20)}{n}} \quad $$ $$ \therefore n = 153.76 $$ $$ \approx 154 $$
Final answer:
The sample size $(n) = 154 $
