Question

) The table shows the number of smokers in a random sample of 500 adults aged 20-24 and the number of smokers in a random sample of 450 adults aged 25-29. Assume that you plan to use a significance level of α = 0.10 to test the claim that p1 ≠ p2. Find the critical value(s) for this hypothesis test. Do the data provide sufficient evidence that the proportion of smokers in the 20 -24 age group is different from the proportion of smokers in the 25-29 age group?

Age 20 -24 Age 25 -29 Number in sample 500 450 Number of smokers 110 63

Answer 1

ANSWER:

Sample proportion of smokers in age 20-24 is =110/500=0.22

Sample proportion of smokers in age 25-29 is =63/450=0.14

pooled proportion=(110+63)/(500+450)=0.1821

Test statistic:

z=(0.22-0.14)/SQRT(0.1821*(1-0.1821)*((1/500)+(1/450)))

z=3.190

critical z value=+/-1.645

Rejection region:z<-1.645 or z>1.645

Reject the null hypothesis.

There is sufficient evidence to conclude that proportion of smokers in 20-24 age group is different from the proportion of smokers in 25-29 age group.

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