Answer:
Given:
Favorable Cases $(x)=25$
Sample Size $(n)=60$
Confidence Interval Level $= 95\%$
Solution:
The Sample Proportion $(\hat{p}):$
$\hat{p} = \frac{25}{60} = 0.4167$
The Significance Level $(\alpha):$
$\alpha = 1 – 0.95 = 0.05$
The critical value $(z_c):$
$z_c = Z_{\alpha/2} = Z_{0.05/2} = 1.96$
The confidence interval $(CI):$
$$CI = \hat{p} \pm z_c \times \sqrt{\frac{\hat{p}(1 – \hat{p})}{n}} $$ $$ = 0.4167 \pm 1.96 \times \sqrt{\frac{0.4167(1 – 0.4167)}{60}} $$ $$ = (0.292, 0.541)$$
Final Answer:
The 95% confidence interval $=(0.292, 0.541)$