Answer:
We accept H₀ sample does not give evidence to support that the proportion of Americans who solely use cell phone differs from 23 %
Step-by-step explanation:
A pew research finds that 23 % ( μ ) of Americans use only cell phone
Sample Information
sample size n = 200
x₁ = 51 then p₁ = 51/200 p₁ = 0,255
and q₁ = 1 - p ₁ q₁ = 1 - 0,255 q₁ = 0,745
Sample big enough for the approximation of the binomial distribution to the normal distribution
p₁*n = 0,255 * 200 = 51 > 5 and q₁*n = 0,745* 200 = 149 > 5
Test hypothesis
Null hypothesis H₀ p₁ = μ = 0,23
Alternative hypothesis Hₐ p₁ ≠ 0,23
Is a two tail test. We choose CI = 95 % then significance level is α = 0,05 %
α = 0,05 as is a two tail test α/2 = 0,025
from z-table z(c) = 1,96
To calculate z(s) = ( x - μ ) /√p₁*q₁/n
z(s) = ( 0,255 - 0,23 )/√0,255*0,745/200
z(s) = 0,025 / 0,0308
z(s) = 0,81
Comparing z(s) and z(c)
z(s) < z(c) 0,81 < 1,96
Then z(s) is in the acceptance region: we accept H₀
