Question

9) In a sample of 88 children selected randomly from one town, it is found 8 of them suffer from asthma. Find the test statistic for a test of claim that the proportion of all children in the town who suffer from asthma is equal to 11%. O Z-0.56 O Z=-0.79 O Z-0.68 O2--0.57

Answer 1

n = 88
x =8

p = 0.11
$\hat{p}=\frac{x}{n}=\frac{8}{88}=0.09091$

Test Statistics :

$Z =\frac{\hat{p}-p}{\sqrt{\frac{p*(1-p)}{n}}}$

$Z=\frac{0.09091-0.11}{\sqrt{\frac{0.11*(1-0.11)}{88}}}$

$Z =\frac{-0.01909}{\sqrt{\frac{0.0979}{88}}}$

$Z=\frac{-0.01909}{\sqrt{0.0011125}}$

$Z=\frac{-0.01909}{0.03335416}$

$Z=-0.572342398$

Answer :     Z = - 0.57