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2 years ago

6

GIVING BRAINLIEST PLEASE HELP!!

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PolarNik [594]2 years ago

3 0

this is really hard but ig that u have to calculate the size of the line

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3 years ago

A Roper survey reported that 65 out of 500 women ages 18-29 said that they had the most say when purchasing a computer; a sample

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Answer:

Step-by-step explanation:

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

<em>Given first random sample size n₁ = 500</em>

Given Roper survey reported that 65 out of 500 women ages 18-29 said that they had the most say when purchasing a computer.

<em>First sample proportion </em>

<em> </em> $p^{-} _{1} = \frac{65}{500} = 0.13$

<em>Given second sample size n₂ = 700</em>

<em>Given a sample of 700 men (unrelated to the women) ages 18-29 found that 133 men said that they had the most say when purchasing a computer.</em>

<em>second sample proportion </em>

<em> </em> $p^{-} _{2} = \frac{133}{700} = 0.19$

<em>Level of significance = α = 0.05</em>

<em>critical value = 1.96</em>

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

<em>Null hypothesis : H₀: There is no significance difference between these proportions</em>

<em>Alternative Hypothesis :H₁: There is significance difference between these proportions</em>

<em>Test statistic </em>

<em></em> $Z = \frac{p_{1} ^{-}-p^{-} _{2} }{\sqrt{PQ(\frac{1}{n_{1} } +\frac{1}{n_{2} } )} }$ <em></em>

<em>where </em>

<em> </em> $P = \frac{n_{1} p^{-} _{1}+n_{2} p^{-} _{2} }{n_{1}+ n_{2} } = \frac{500 X 0.13+700 X0.19 }{500 + 700 } = 0.165$ <em></em>

<em> Q = 1 - P = 1 - 0.165 = 0.835</em>

<em></em> $Z = \frac{0.13-0.19 }{\sqrt{0.165 X0.835(\frac{1}{500 } +\frac{1}{700 } )} }$ <em></em>

<em>Z = -2.76</em>

<em>|Z| = |-2.76| = 2.76 > 1.96 at 0.05 level of significance</em>

<em>Null hypothesis is rejected at 0.05 level of significance</em>

<em>Alternative hypothesis is accepted at 0.05 level of significance</em>

<u><em>Conclusion:</em></u><em>-</em>

<em>There is there is a difference between these proportions at α = 0.05</em>

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