Respuesta :
Answer:
The calculated value Z = 3.775 > 1.96 at 0.05 level of significance
Null hypothesis is rejected
The Two Population proportion are not equal
Step-by-step explanation:
Given first sample size n₁ = 677
First sample proportion
[tex]p^{-} _{1} = \frac{x_{1} }{n_{1} } = \frac{172}{677} = 0.254[/tex]
Given second sample size n₂ = 3377
second sample proportion
[tex]p^{-} _{2} = \frac{x_{2} }{n_{2} } = \frac{654}{3377} = 0.1936[/tex]
Null Hypothesis : H₀ : p₁ = p₂.
Alternative Hypothesis : H₁ : p₁ ≠ p₂.
Test statistic
[tex]Z = \frac{p_{1} ^{-}-p^{-} _{2} }{\sqrt{P Q(\frac{1}{n_{1} } +\frac{1}{n_{2} }) } }[/tex]
where
[tex]P = \frac{n_{1} p_{1} + n_{2} p_{2} }{n_{1}+n_{2} } = \frac{677 X 0.254+3377 X 0.1936}{677+3377}[/tex]
P = 0.2036
Q = 1 - P = 1 - 0.2036 = 0.7964
[tex]Z = \frac{0.254- 0.1936 }{\sqrt{0.2036 X 0.7964(\frac{1}{677 } +\frac{1}{3377 }) } }[/tex]
Z = 3.775
Critical value ∝=0.05
Z- value = 1.96
The calculated value Z = 3.775 > 1.96 at 0.05 level of significance
Null hypothesis is rejected
The Two Population proportion are not equal
