A sample of 200 light bulbs was tested and it was found that 11 were defective.Calculate a 95% confidence interval around this sample proportion.
A)$0.055 \pm 1.96$
B)$0.055 \pm 0.016$
C)$0.055 \pm 0.032$
D) $11 \pm 1.96$
E)$200 \pm 11$

Question

Quizplus · Accepted Answer

To calculate the confidence interval for proportion, use the formula:
$$ 	ext{Confidence interval} = \hat{p} \pm z_{\alpha/2} \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}$$
where $\hat{p}$ is the sample proportion, $z_{\alpha/2}$ is the critical value for the desired confidence level (in this case, 95%), and $n$ is the sample size.

Plugging in the given values, we have:
$$ 	ext{Confidence interval} = 0.055 \pm 1.96 \sqrt{\frac{0.055(1-0.055)}{200}}$$
Simplifying this expression gives:
$$ 	ext{Confidence interval} = 0.055 \pm 0.032 $$
Therefore, the best choice is C.

A Sample of 200 Light Bulbs Was Tested and It 0.055±1.960.055 \pm 1.960.055±1.96

A Sample of 200 Light Bulbs Was Tested and It $0.055 \pm 1.96$