Question

Express the confidence interval (0.036, 0.086) in the form of p-e< p

Answer 1

p-e< p < p+e

(0.061 - 0.025) < 0.061 < (0.061 + 0.025)

0.036 < 0.061 < 0.086

Explanation:

Given;

Confidence interval CI = (a,b) = (0.036, 0.086)

Lower bound a = 0.036

Upper bound b = 0.086

To express in the form;

p-e< p < p+e

Where;

p = mean Proportion

and

e = margin of error

The mean p =( lower bound + higher bound)/2

p = (a+b)/2

Substituting the values;

p = (0.036+0.086)/2

Mean Proportion p = 0.061

The margin of error e = (b-a)/2

Substituting the given values;

e = (0.086-0.036)/2

e = 0.025

Re-writing in the stated form, with p = 0.061 and e = 0.025

p-e< p < p+e

(0.061 - 0.025) < 0.061 < (0.061 + 0.025)

0.036 < 0.061 < 0.086