The number of years it took a random sample of 33 former smokers to quit permane

Question

The number of years it took a random sample of 33 former smokers to quit permanently it listed. We know that the population standard deviation is 1.5 years. A health agency claims that the mean time it takes smokers to quit smoking permanently is 6 years. You think it’s more than that. At , is there enough evidence to reject the health agency’s claim? At the 1% level? Can you test the claim using an appropriate CI? Explain. If your answer is yes, test the claim that way, too

Smokers Years to quit smoking 1 10.7 2 3.2 3 12.6 4 9 5 8.7 6 9.2 7 0.7 8 3 9 2.3 10 8.2 11 12.8 12 9.8 13 3.3 14 1.8 15 0.8 16 1 17 2.5 18 8.1 19 20.7 20 12.5 21 9.9 22 2.9 23 7.1 24 8.3 25 5.2 26 7 27 7.8 28 0.1 29 3.5 30 10.5 31 4.2 32 1.1 33 6.1

Explanation / Answer

here null hypothesis: mean =6

alternate hypothesis:mean>6

for p value for above test is greater then 0.01 level we can not reject null hypothesis that it takes 6 years for a smoker to quit smoking

for 98% confidence interval and (n-1=32) degree of freedom t=2.7385

hence 98% confidence interval =sample mean -/+ t*Std error =4.2979 ; 8.7081

as above interval contains 6 as probable value of number of year to quit smoking

we can not reject null hypothesis that it takes 6 years for a smoker to quit smoking

X 10.7 3.2 12.6 9 8.7 9.2 0.7 3 2.3 8.2 12.8 9.8 3.3 1.8 0.8 1 2.5 8.1 20.7 12.5 9.9 2.9 7.1 8.3 5.2 7 7.8 0.1 3.5 10.5 4.2 1.1 6.1 mean(X) 6.503 std deviation(S) 4.626 std error =S/(n)1/2 0.805 t=(X-6)/std error 0.625 p value 0.268

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