Let P1 be the proportion of successes in the first population and let P2 be the...

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Let P1 be the proportion of successes in the first population and let P2 be the proportion of successes in the second populat

math Statistics-And-Probability

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Answer 1

Answer #1

Solution:

Given:

$H_{0}: p_{1}-p_{2}=0$

$H_{a}: p_{1}-p_{2} \neq 0$

Since Ha is not equal to type this is two tailed test.

z test statistic = z* = 1.73

We have to find p-value.

For two tailed test , p-value is:

p-value = 2* P(Z > z test statistic) if z is positive

p-value = 2* P(Z < z test statistic) if z is negative

thus

p-value = 2* P(Z > z test statistic)

p-value = 2* P(Z > 1.73)

p-value = 2* ( 1 - P(Z < 1.73) )

Look in z table for z = 1.7 and 0.03 and find corresponding area.

z .00 .01 .02 .03 .04 .05 .06 .07 .08 .09 5120 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 .5000

P( Z< 1.73 )= 0.9582

thus

p-value = 2* ( 1 - P(Z < 1.73) )

p-value = 2* ( 1 - 0.9582 )

p-value = 2* 0.0418

p-value = 0.0836

Thus required answer for p-value is: 0.0836

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Answer 2

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