Question

A student wants to survey the sophomore class of 200 students about whether the school should require uniforms. A

Answer 1

Answer: C

Step-by-step explanation:

Given:

Sample size (n) = 50

x = 12

$\widehat{\mathbf{p}}=\frac{\mathbf{x}}{n}=\frac{12}{50}=0.24$

Confidence level = 90%

α = 1 − 0.90 = 0.10

α/2 = 0.05

$\text { Critical value }\left(z_{c}\right)=z_{\frac{\alpha}{2}}=z_{0.05}=1.6449$

(from standard normal table)

90% Confidence interval is,

$\begin{aligned}&\text { Confidence interval }=\widehat{\mathbf{p}} \pm z_{c} \times \sqrt{\frac{\hat{\mathbf{p}}(1-\hat{\mathbf{p}})}{n}} \\&\text { C. I }=0.24 \pm 1.6449 \times \sqrt{\frac{0.24(1-0.24)}{50}} \\&\text { C. I }=0.24 \pm 1.65 \times \sqrt{\frac{0.24(1-0.24)}{50}}\left\end{aligned}$

Therefore, 90% confidence interval for the true proportion of sophomores who favour the adoption of uniforms is C