Answer:
CI = ( 0,539 ; 0,599)
Step-by-step explanation:
The proportion p₀ of person that hung up the phone in the first minute of waiting is:
p₀ = 569/1000 p₀ = 0,569 p₀ = 56,9 %
Then q₀ = 1 - 0,569 q₀ = 0,431 q₀ = 43,1 %
Sample size is n = 1000
A 95 % CI is: α = 5 % α = 0,05 a/2 = 0,025
In z-table we look z ( score ) for 0,025 z = ± 1,96
Now CI for proportion is:
p₀ - z (α/2) * √ (p₀*q₀ )/n < p < p₀ + z (α/2) * √ (p₀*q₀ )/n
we need to find out
z(α/2) * √ (p₀*q₀ )/n = 1,96*√ ( 0,569*0,431)/1000 = 1,96 *0,01566 =0,03
Then
CI ( 95%) = 0,569 ± 0,03 = ( 0,569 - 0,03 ; 0,569 + 0,03)
CI = ( 0,539 ; 0,599)
