Question

In a simple random sample of 80 patients who saw a certain dentist nine patients had their teeth whitened.

Which interval is the 95% confidence interval for the percent of all this dentist patients who had their teeth whitened
4.4,18.2
8.4,14.2
5.5, 17.1
7.8, 14.8

Answer 1

The correct option is 1.

Explanation:

The total number of patient is 80 and out of these patients 9 patients had their teeth whitened.

The confidence interval is 95%.

The probability of patient had teeth whitened is

`p=(9)/(80)`

The z-score for 95% confidence interval is 1.96.

The confidence limit is defined as

`E=p\pm \sqrt{(p(1-p))/(n)}* z*`

`E=0.1125\pm \sqrt{(0.1125(1-0.1125))/(80)}* 1.96`

`E=0.043,0.182`

These values are in percent.

`[0.043* 100,0.182* 100]`

`[4.3,18.2]`

Therefore option 1 is correct.