Assume that the samples are independent In a random sample o

Assume that the samples are independent. In a random sample of 500 people aged 20-24, 22% were smokers. In a random sample of 450 people aged 25-29, 14% were smokers. Test the claim that the proportion of smokers in the two age groups in the different. Use significance level of 0.10. Null and Alternative Hypothesis Test Statistic Critical Value(s) P-Value State the final conclusion that addresses the original claim

Solution

a.
Null Hypothesis : p1 = p2
Alternate Hypothesis: p1 != p2

b.
Pooled sample proportion p = (p1 * n1 + p2 * n2) / (n1 + n2)
= (0.22*500 + 450*0.14)/(500+450)
= 0.1821

Standard Error SE = sqrt{ p * ( 1 - p ) * [ (1/n1) + (1/n2) ] }
= sqrt(0.1821 * (1-0.1821) * (1/500+1/450))
=0.0251

Test Static z = (p1 - p2) / SE
=(0.22-0.14)/0.0251
= 3.1873 Answer

c.
Critical Values:
Since we have a two-tailed test, the P-value is the probability that the z-score is less than -3.1873 or greater than 3.1873.

d.
P-value = 2*(1-0.9993) = 0.0014 Answer

e.
alpha =0.10
Since P-value < 0.10
We will reject null hypothesis.