Question

In a sample of 200 adults, 68 complain they suffer from insomnia. Calculate the 95% confidence interval for this proportion. Interpret what this means.

Answer 1

Solution:

Confidence interval for Population Proportion is given as below:

Confidence Interval = P ± Z* sqrt(P*(1 – P)/n)

Where, P is the sample proportion, Z is critical value, and n is sample size.

We are given

x = 68

n = 200

P = x/n = 68/200 = 0.34

Confidence level = 95%

Critical Z value = 1.96

(by using z-table)

Confidence Interval = P ± Z* sqrt(P*(1 – P)/n)

Confidence Interval = 0.34 ± 1.96* sqrt(0.34*(1 – 0.34)/200)

Confidence Interval = 0.34 ± 1.96* 0.0335

Confidence Interval = 0.34 ± 0.0657

Lower limit = 0.34 - 0.0657 = 0.2743

Upper limit = 0.34 + 0.0657 = 0.4057

Confidence interval = (0.2743, 0.4057)

We are 95% confident that the population proportion of the adults who suffer from insomnia will be lies between 0.2743 and 0.4057.