Use the traditional method to test the given hypothesis.Assume that the samples

Question

Use the traditional method to test the given hypothesis.Assume that the samples are independent and that they havebeen randomly selected.
In a random sample of 500 people aged 20-24,22% were smokers.In a random sample 450 people aged 25-29, 14% were smokers.Test the claim that the proportion of smokers in the two age groupsis the same. Use a significance level of 0.01



Use the traditional method to test the given hypothesis.Assume that the samples are independent and that they havebeen randomly selected.
In a random sample of 500 people aged 20-24,22% were smokers.In a random sample 450 people aged 25-29, 14% were smokers.Test the claim that the proportion of smokers in the two age groupsis the same. Use a significance level of 0.01

Explanation / Answer

aged 20-24: n1=500, p1=0.22 aged 25-29: n2=450, p2=0.14 =0.01, Z(0.005)=2.58 (check normal table) The test hypothesis is Ho:p1=p2 Ha:p1 not equal p2 The test statistic is Z=(p1-p2)/[p1*(1-p1)/n1 + p2*(1-p2)/n2] =(0.22-0.14)/sqrt(0.22*(1-0.22)/500 + 0.14*(1-0.14)/450) = 3.24 Since Z=3.24 > 2.58, we reject Ho. So we can not conclude thatthe proportion of smokers in the two age groups is the same

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