Answer:
<em>The test statistic value Z = 4.64 > 1.96 at 0.05 level of significance</em>
<em>Null hypothesis is rejected </em>
<em>Alternative hypothesis is accepted</em>
<em>Test the claim that the proportion of all children in the town who suffer not from asthma is 11%</em>
Step-by-step explanation:
<u><em>Step(i):-</em></u>
Given sample size 'n' = 167
Given data In a sample of 167 children selected randomly from one town, it is found that 37 of them suffer from asthma.
<em>Sample proportion </em>
![p^{-} = \frac{x}{n} = \frac{37}{167} = 0.2215](https://tex.z-dn.net/?f=p%5E%7B-%7D%20%20%3D%20%5Cfrac%7Bx%7D%7Bn%7D%20%3D%20%5Cfrac%7B37%7D%7B167%7D%20%3D%200.2215)
<em>Given Population proportion 'P'</em> = 11% = 0.11
<u><em>Step(ii) </em></u>:-
<em>Null Hypothesis : H₀ : p = 11</em>
<em>Alternative Hypothesis H₁: p≠11</em>
<u><em>Test statistic</em></u>
![Z = \frac{p^{-} -P }{\sqrt{\frac{P Q}{n} } }](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7Bp%5E%7B-%7D%20-P%20%7D%7B%5Csqrt%7B%5Cfrac%7BP%20Q%7D%7Bn%7D%20%7D%20%7D)
![Z = \frac{0.2215 -0.11 }{\sqrt{\frac{0.11 X 0.89}{167} } }](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7B0.2215%20-0.11%20%7D%7B%5Csqrt%7B%5Cfrac%7B0.11%20X%200.89%7D%7B167%7D%20%7D%20%7D)
Z = 4.64
<u><em>step(iii)</em></u>
<em> Critical value Z = 1.96 </em>
<em>The calculated value Z = 4.64 > 1.96 at 0.05 level of significance</em>
<em>Null hypothesis is rejected </em>
<em>Alternative hypothesis is accepted</em>
<u><em>Conclusion:-</em></u>
<em>Test the claim that the proportion of all children in the town who suffer not from asthma is 11%</em>