You are testing the claim that the proportion of men who own cats is smaller than...

You are testing the claim that the proportion of men who own cats is smaller than the proportion of women who own cats.

You sample 180 men, and 75% own cats.

You sample 120 women, and 15% own cats.

Find the test statistic, rounded to two decimal places.

Expert Solution

Null hypothesis

H0:P1=P2

Alternative hypothesis
H1:P1<P2


We have given for the example

x1=135
n1=180

x2=18
n2=120

Estimate for sample proportion 1 $=\hat{p}_{1}=0.75$

Estimate for sample proportion 2 $=\hat{p}_{2}= 0.15$

Pooled proportion $=\bar{P}=0.51$

Z test statistic formula is

$Z=\frac{\hat{p}_{1}-\hat{p}_{2}}{\sqrt{\bar{P}\bar{Q}\left ( \frac{1}{n_{1}}+\frac{1}{n_{2}} \right )}}$

$=\frac{0.75-0.15}{\sqrt{(0.51*(1-0.51))\left ( \frac{1}{180}+\frac{1}{120} \right )}}$

=10.18

orchestra answered 2 years ago

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