Question

Chapter 6, Section 3-HT, Exercise 158 - MathPad Test whether people with a specific genetic marker are more likely to have suffered from clinical depression than people without the genetic marker, using the information that 40% of the 40 people in a sample with the genetic marker have had dinical depression while 16 of the 750 people in the sample without the genetic marker have had clinical depression Use subscripts for yes these people have the genetic marker and 2 for no these people do not have the genetic marker (a) Find the relevant sample proportions in each group and the pooled proportion Round your answers to three decimal places, if necessary P =

Answer 1

$\hat{p}_1$ = 16 / 40 = 0.4

$\hat{p}_2$ = 120 / 750 = 0.16

$\hat{p}$ = (120 + 16) / 40 + 750) = 136 / 810 = 0.172

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The Hypothesis:

H0: p₁ = p₂

Ha: p₁ > p₂

This is a 2 Tailed Test.

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The Test Statistic:

$Z = \frac{p1-p2}{\sqrt{\hat{p}(1-\hat{p})(\frac{1}{n1}+\frac{1}{n2})}} = \frac{0.4-0.16}{\sqrt{0.172*0.827*(\frac{1}{40}+\frac{1}{750})}} = 3.92$

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The p Value: The p value (2 Tail) for Z = 3.92, is; p value = 0.000

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Since p value is very small, We Reject H0.

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