Question

6. During an independent research, 2500 randomly selected people were interviewed whether they visit their dentist for a regular dental checkup or not. Only 2000 gave a positive answer. Calculate a 95% two-sided confidence interval on the proportion of people who regularly have a dental checkup.

Answer 1

0.80+/- 0.016

(0.784, 0.816)

The 95% confidence interval on the proportion of people who regularly have a dental checkup is = (0.784, 0.816)

Explanation:

Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.

The confidence interval of a statistical data can be written as.

p+/-z√(p(1-p)/n)

Given that;

Proportion p = 2000/2500 = 0.80

Number of samples n = 2500

Confidence interval = 95%

z-value(at 95% confidence) = 1.96

Substituting the values we have;

0.80+/- 1.96√(0.80(1-0.80)/2500)

0.80+/- 1.96√(0.000064)

0.80+/- 0.01568

0.80+/- 0.016

(0.784, 0.816)

The 95% confidence interval on the proportion of people who regularly have a dental checkup is = (0.784, 0.816)