Question

Construct a 96% confidence interval for the true proportion of professional baseball players who use performance-enhancing drugs (PEDs) if an anonymous simple random sample of 250 professional players showed that 50 of them used PEDs.

Answer 1

Solution:
Given that, n=250,x=50
p^=x/n
=50/250
p^=0.2
(1–α)%=96%
α=0.04
α/2=0.02
Zα/2=2.05 ....... from standard normal table.
Margin of error=E=Zα/2 ×√{[p^(1-p^)]/n}
=2.05 ×√{[0.2(1-0.2)]/250}
=0.0519
Margin of error=E=0.0519
95% confidence interval for the population proportion p is given as,
p^ ± Margin of error=(0.2-0.0519,0.2+0.0519)
=(0.1481,0.2519)
Lower limit =0.1481
Upper limit=0.2519