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Whitepunk [10]
3 years ago
12

Assume that you plan to use a significance level of α = 0.05 to test the claim that p1 = p2. Use the given sample sizes and numb

ers of successes to find the pooled estimate. Round your answer to the nearest thousandth.
n1 = 677 n2 = 3377
x1 = 172 x2 = 654
Mathematics
1 answer:
dezoksy [38]3 years ago
3 0

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

<u>Step-by-step explanation</u>:

<em>Given first sample size n₁ = 677</em>

<em>First sample proportion </em>

<em>                              </em>p^{-} _{1} = \frac{x_{1} }{n_{1} } = \frac{172}{677} = 0.254<em></em>

Given second sample size n₂ = 3377

<em>second sample proportion </em>

<em>                              </em>p^{-} _{2} = \frac{x_{2} }{n_{2} } = \frac{654}{3377} = 0.1936<em></em>

<u><em>Null Hypothesis : H₀ :</em></u><em>  p₁ = p₂.</em>

<u><em>Alternative Hypothesis : H₁</em></u><em> :  p₁ ≠ p₂.</em>

      Test statistic

                Z = \frac{p_{1} ^{-}-p^{-} _{2}  }{\sqrt{P Q(\frac{1}{n_{1} } +\frac{1}{n_{2} }) } }

where

        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}

       P =  0.2036

      Q = 1 - P = 1 - 0.2036 = 0.7964

       

         Z = \frac{0.254- 0.1936 }{\sqrt{0.2036 X 0.7964(\frac{1}{677 } +\frac{1}{3377 }) } }

        Z =  3.775

<em>Critical value ∝=0.05</em>

<em>Z- value = 1.96</em>

<em>The calculated  value Z = 3.775 > 1.96 at 0.05 level of significance</em>

<em>Null hypothesis is rejected </em>

<em>The Two Population proportion are not equal</em>

<em></em>

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