Question

What proportion of asthma patients are allergic to house dust? In a sample of 140, 35 percent had positive skin reactions. Construct the 95 percent confidence interval for the population proportion.

Answer 1

Here we have that

n = 140

p = 0.35

significance level = 1 – confidence = 1 – 0.95 = 0.05

Critical z-value $z_{\alpha/2}=z_{0.05/2}=z_{0.025} =1.96$ from standard normal table.

Confidence interval:

$p\pm z_{\alpha/2}\sqrt{\frac{p(1-p)}{n}}=0.35\pm1.96\sqrt{\frac{0.35\cdot0.65}{140}}=0.35\pm0.08$

The 95% confidence interval for the population proportion is (0.27, 0.43).