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.

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* \sqrt{(p(1-p))/(n)}\\\\=1.96* \sqrt{(0.32* 0.68)/(1200)}\\\\=1.96* 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.