Respuesta :
Answer:
We accept with 99 % of confidence that p₁ ( the proportion in the group aged 18 - 34 ) is bigger than p₂ (the proportion in the group aged 35-44)
Step-by-step explanation:
Group aged 18 - 34
Sample size n₁ = 655 sample size enough to apply a normal distribution aproximation for the test
p₁ = 0,45 and q₁ = 1 - p₁ q₁ = 0,55
p₁*n₁ = 0,45*655 = 294 q₁*n₁ = 0,55*655 = 360
both bigger than 5
p₁ = 45 % or p₁ = 0,45 then q₁ = 1 - 0,45 q₁ = 0,55
Group aged 35 - 44
Sample size n₂ = 420 sample size enough to apply a normal distribution aproximation for the test
p₂ = 37% p₂ = 0,37 and q₂ = 0,63
p₂*n₂ = 0, 37*420 = 155 q₁*n₁ = 0,63*420 = 264
Test Hypothesis
Null Hypothesis H₀ p₁ = p₂
Alternative Hypothesis Hₐ p₁ > p₂
Significance level α = 1% α = 0,01
Confidence Interval CI = 99 %
Then from z table we find critical z z (c ) = 3,1
Calculating z(s)
z(s) = ( p₁ - p₂ )/ √[ ( p₁*q₁)/n₁ ] + [ (p₂*q₂)/n₂ ]
z(s ) = (0,45 - 0,37 ) / √ 0,45*0,55)/655 + 0,37*0,63 /420
z(s) = 0,08 /0,03
z(s) = 2,66
Comparing z(s) and z(c)
z(s) < z(c)
Then z (s) is inside the acceptance region for H₀
