Question

A random sample of 450 vacationers in a huge luxury resort showed that 150 were business executives. We want to create a 95% confidence interval for the proportions of vacationers who are business executives.

a) What is the value at the centre of the 95% confidence interval? Write the symbol and value.

Answer 1

p(s) = 0,33

Explanation:

n = 450

p₀ = 150/450 p₀ = 0,33 then q₀ = 0,67

n*p₀ = 0,33*450 = 150

n*q₀ = 0,67*450 = 301

n*p₀ and n*q₀ more than 10, we can approximate the binomial to a Normal Distribution Distribution

a) p - p₀ = z(c) * √ (p₀q₀)/n

z(c) = ??

CI 95 % then α = 5 % α = 0,05 α/2 = 0,025

z(c) = 1,96

p = p₀ ± z(c) * √ (p₀q₀)/n

p = 0,33 ± 1,96 * 0,022

p = ( 0,33 - 0,04 ; 0,33 + 0,04

p = ( 0,29 ; 0,37 )

The value of the center of the confidence Interval is 0,33

p(s) = 0,33