Question

2.Drug use. A Department of Health and Human Services study of illegal drug use among 12- to 17-year-olds reported a decrease in use (from 11.4% in 1997 to 9.9% now). Suppose a survey in a large high school reveals that, in a random sample of 1,050 students, 98 report using illegal drugs. Test the principal’s claim that illegal drug use in her school is below the current national average. Use a 0.05 significance level and conduct a full hypothesis test using the six-step process.

Answer 1

Solution-1:

step1:

State Ho and Ha

Ho=0.099

Ha:p<0.099

illegal drug use in her school is below the current national average

Ha is the claim

Step2:

level of signifcance=0.05

step3:

decision rule if

z critical in excel

=NORM.S.INV(0.05)

=-1.644853627

if z <-1.645 reject Ho else if z>-1.645 Do not reject Ho

or if p<0.05 reject Ho or if p>0.05 fail to reject Ho

step4:

test statistic:

z=p^-p/sqrt(p*(1-p)/n

p^=x/n=98/1050=0.09333333

z=(0.09333333-0.099)/sqrt(0.099*(1-0.099)/1050)

z=-0.6148123

step5:

statistical decision

test statistic >critical z value

-0.6148123>-1.645

Fail to reject Ho

also p=0.2693

p>0.05

Fail to reject Ho

Step6:

conclusion:

There is no suffcient statistical evidence at 5% level of significance to conclude that illegal drug use in her school is below the current national average