Respuesta :
Answer:
We know that at CI of 90% the new study provide evidence to claim that the porcentage of multigenerational households has not change
Step-by-step explanation:
To use Normal Distribution as an approximation of the binomial distribution
and develop a test of proportion we look at the products:
n*p and n*q in the sample
p = 28/580 p = 0,04827 then q = 0,95173
and n*p = 580*0,04827 = 27,99 > 5
n*q = 580*0,95173 = 552 > 5
Hypothesis Test:
p₀ = 4 % p₀ = 0,04
sample size n = 580
p sample proportion mean p = 0,04
Chossing a confidence Interval CI = 90 % then α = 10% α = 0,1
α/2 = 0,05 and z(score) = 1,64 z (c) = 1,64
The test is a doble tail test since the question is about difference between the study and the past census
Null Hypothesis H₀ p = p₀
Alternative Hypothesis Hₐ p ≠ p₀
To calculate z(statistics) z(s)
z(s) = ( p - p₀ ) / √ p*q/n
z(s) = ( 0,04827 - 0,04 ) * √580 / √0,04827*0,95173
z(s) = 0,00827*24,08/ √0,04594
z(s) = 0,1991/ 0,2143
z(s) = 0,929
Comparing z(s) and z(c)
z(s) < z(c) ; 0,929 < 1,64
Therefore at CI 90% we accept H₀ since z(s) is in the acceptance region
