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

Answer:

p(s) = 0,33

Step-by-step 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