4. In the past decades there have been intensive antismoking...

4. In the past decades there have been intensive antismoking campaigns sponsored by both federal and private agencies. In one study of national smoking trends, two random samples of U.S. adults were selected in different years: The first sample, taken in 1995, involved 4276 adults, of which 1642 were smokers. The second sample, taken in 2010, involved 3908 adults, of which 1415 were smokers. (a) (4 points) Construct a 98% confidence interval for the difference in the proportions of all U.S. adults that smoked between 1995 and 2010.

Transcript

00:01 Hi, i'm david and i'm here to help you answer your question.

00:03 Now let me bring up your question here.

00:07 In this question we discuss about the confident interval between the two proportions.

00:13 Let me remind you that the comforting interval for the p1 minus p2.

00:19 It will be the phod 1 minus ph2 plus and minus the z and 4 over 2 times square root of the p1 times 1 minus p1 over n1 plus p2 times 1 minus p2 number and 2 and if we don't know the two proportion we can use the estimated 1 here and now in this question here we can summarize the question is following here we have the group 1 and the group 2 here so the n and the number of the x success here then we will have the p heart here so for the first sample we will have equal to the end equal to the 4276 and the number here we have the 164 2.

01:18 Therefore we can compute the phearts 1 equal to the 164 2 divided by 4276.

01:27 If we do the calculation, we get the 16424, divided by the 4276 get equal to the 0 .384 now for the second one we have the 3908 and finally we have the 1 415 and if we compute the ph 2 equal to 1 415 divided by the 3908 and then we get the ph 2 equal to 1 415 and then we get the ph 2 equal to 415 divided by 3908 get equal to the 0 .362 and here we want to find the 98 % comfort interval so means that alpha equal to the 100 % minus 98 % equal to 2 % so the 4 and 5 % it will equal to alpha equal to 1 % therefore to find the z -upon -0 -0 -1 to find the value z there i will bring up the z -table i will show you how to use the z table here let me put the z table on here next to each here so let me put the table here and now we will see for the values upon zero one we see it will be zero point zero one it will be this value closest one, we turn the 2 .33.

03:11 And then we will be able to compute the competitive interval now.

03:17 So by formula the 98 % complete interval for v1 minus p2, it will be behind 1 minus behind 2, it will be 0 .384 minus 0 .362 and then plus and minus z 2 .33 times the square root.

03:42 B .hat 1 will be 0 .384 times 1 minus 0 .384...

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