Question

Eric wants to estimate the percentage of elementary school children who have a social media account. He surveys 450 elementary school children and finds that 280 have a social media account. Identify the values needed to calculate a confidence interval at the 99% confidence level. Then find the confidence interval.

Answer 1

(0.597, 0.643)

Explanation:

I took the quiz :)

Answer 2

Answer with explanation:

The confidence interval for population mean is given by :-

`\hat{p}\pm z_(\alpha/2)\sqrt{\frac{\hat{p}(1-\hat{p})}{n}}`

, where
`\hat{p}` is the sample proportion, n is the sample size ,
`z_(\alpha/2)` is the critical z-value.

The values needed to calculate a confidence interval at the 99% confidence level are :

Given : Significance level :
`\alpha:1-0.99=0.01`

Sample size : n=450

Critical value :
`z_(\alpha/2)=2.576`

Sample proportion:
`\hat{p}=(280)/(450)\approx0.62`

Now, the 99% confidence level will be :

`\hat{p}\pm z_(\alpha/2)\sqrt{\frac{\hat{p}(1-\hat{p})}{n}}\\\\=0.62\pm(2.576)\sqrt{(0.62(1-0.62))/(450)}\\\\\approx0.62\pm0.023\\\\=(0.62-0.023,\ 0.62+0.023)=(0.597,\ 0.643)`

Hence, the 99% confidence interval is
`(0.597,\ 0.643)`