Question

20) In a recent poll of 1200 randomly selected adult office workers, 32% said they had worn a Halloween costume to the office at least once. Report the 95% confidence interval for the proportion of all adult office workers who have worn a Halloween costume to the office at least once. (Round final calculations to the nearest tenth of a percent) A) (30.7%, 33.4%) B) (28.0%, 36.1%) C) (29.4%, 34.6%) D) None of these

Answer 1

Answer: Option 'c' is correct.

Step-by-step explanation:

Since we have given that

n = 1200

x = 32% of 1200

So, $\hat{p}=32\5=0.32$

We need to find 95% confidence interval.

so, z = 1.96

So, margin of error would be

$z\times \sqrt{\dfrac{p(1-p)}{n}}\\\\=1.96\times \sqrt{\dfrac{0.32\times 0.68}{1200}}\\\\=1.96\times 0.0135=$

So, Interval would be

$\hat{p}\pm \text{margin of error}}\\\\=0.32\pm 0.0263\\\\=(0.32-0.0263,0.32+0.0263)\\\\=(0.2937,0.3463)\\\\=(0.294,0.346)\\\\=(29.4\%,34.6\%)$

Hence, Option 'c' is correct.