Answer:
Given:
The Population Proportion $ (p) = 0.28 $
The Margin Of Error $ (E) = 0.02 $
The Confidence Interval Level $ = 90\% $
Solution:
The Significance Level $ (\alpha) : $
$ \alpha = 1- 0.90 $
$ = 0.10 $
The Critical Value $ (z_c): $
$ z_c = z_{\alpha/2} $
$ = z_{0.10/2} $
$ = 1.645 $
→ Here we use a margin of error formula to find out the sample size
$ E = z_c \times \sqrt{\frac{p \times (1 – p)}{n}} $
$ 0.02 = 1.645 \times \sqrt{\frac{0.28 \times (1 – 0.28)}{n}} $
$ n = 1355.56 $
$ n \approx 1356 $
Final Answer:
The sample size $ (n) = 1356 $