Identify the null hypothesis, alternative hypothesis, test statistic, critical value(s), P-value, conclusion about the null

hypothesis, and final conclusion that addresses the original claim. Also include a diagram with critical regions marked.

1) In a sample of 167 children selected randomly from one town, it is found that 37 of them suffer from asthma. At

the 0.05 significance level, test the claim that the proportion of all children in the town who suffer from asthma

is 11%.

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by Level 10 User (57.4k points)

H0: p=0.11 (the claim)

Ha: p≠0.11 (counterclaim)

q=1-p=0.89

Sample p hat=37/167=0.2216 approx (22.16%)

Sample n=167

Test statistic for test: (p hat-p)/√(pq/n)=

(0.2216-0.11)/0.0242=0.1116/0.0242=4.607.

The probability associated with this value is about 0.000 (p-value) from which we conclude (the critical probability is 0.025) that we reject H0 and default to Ha, the proportion is not 11%.

by Top Rated User (680k points)