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fredd [130]
2 years ago
14

Let n1=50​, X1=10​, n2=50​, and X2=30. Complete parts​ (a) and​ (b) below. a. At the 0.10 level of​ significance, is there evide

nce of a significant difference between the two population​ proportions? Determine the null and alternative hypotheses. Choose the correct answer below. A. H0: π1≤π2 H1: π1>π2 B. H0: π1≠π2 H1: π1=π2 C. H0: π1≥π2 H1: π1<π2 D. H0: π1=π2 H1: π1≠π2 Your answer is correct. Calculate the test​ statistic, ZSTAT​, based on the difference p1−p2. The test​ statistic, ZSTAT​, is nothing.
Mathematics
1 answer:
iren2701 [21]2 years ago
3 0

Answer:

|Z| = |-4.089| > 1.645 at 0.10 level of significance

Null hypothesis is rejected at  0.10 level of significance

<em>There is a difference between the two Population proportions</em>

Step-by-step explanation:

<u><em>Step(i)</em></u>:-

Given first sample size (n₁)  = 50

Given  proportion of the first sample p⁻₁= 0.2

Given second sample size (n₂)  = 50

Given proportion of the second sample p₂⁻ = 30/50 = 0.6

<em>Null Hypothesis : H₀: p₁⁻=p₂⁻</em>

<em>Alternative Hypothesis : H₁: p₁⁻≠p₂⁻</em>

<u><em>Step(ii):-</em></u>

Z-statistic

             Z = \frac{p_{1} -p_{2} }{\sqrt{pq(\frac{1}{n_{1} } +\frac{1}{n_{2}) } } }

Where

         P = \frac{n_{1}p_{1} +n_{2}  p_{2} }{n_{1} +n_{2} }

        P = \frac{50X0.2+50X0.6}{50+50} = 0.4

<em>Z-statistic</em>

       

      Z = \frac{0.2-0.6}{\sqrt{0.4 X 0.6(\frac{1}{50}+\frac{1}{50}  } }

     Z =  -4.089

Level of significance =0.10

Z₀.₁₀ = 1.645

|Z| = |-4.089| > 1.645 at 0.10 level of significance

Null hypothesis is rejected at  0.10 level of significance

<u><em>Final answer</em></u>:-

<em>There is a difference between the two Population proportions</em>

   

     

       

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