Yolanda & Garmin conducted a study with a random sample of 45 asthmatic children

Question

Yolanda & Garmin conducted a study with a random sample of 45 asthmatic children. The parents of each asthmatic child completed a questionnaire about their home environment. The researchers discovered that 18 of the asthmatic children lived in homes with dust mites or cockroaches present during the past 12 months. Is this sufficient evidence to conclude that greater than 35 percent of the population of asthmatic children live in homes with dust mites or cockroaches present? Let = 0.05. Use both the critical value and p-value methods, and show all 5 steps.

Explanation / Answer

n=45, x=18 , p=x/n=18/45=0.4

null hypothesis H0: P=0.35 and

alternate hypotheiss H1: P>0.35 ( one tailed test)

SE(P)=sqrt(p(1-p)/n)=sqrt(0.35*(1-0.35)/45)=0.0711

test statistic z=(P-p)/SE(P)=(0.45-0.35)/(0.0711)=1.41

level of significance alpha=0.05

critical region z>z(0.05)=1.6449

since calcuated z doesnot belong to critical region so we fail to reject H0 and conclude that there is not sufficient evidence to conclude that greater than 35 percent of the population of asthmatic children live in homes with dust mites or cockroaches present.

since p-value=0.08 is more than alpha=0.05, so we fail to reject H0

p-value=0.08

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