Time April 18 1994 reported the results of a telephone poll

Time, April 18, 1994, reported the results of a telephone poll of 800 adult Americans, 605 of them nonsmokers, who were asked the following question: “Should the federal tax on cigarettes be raised by $1.25 to pay for health care reform?” Let 1 and 2 be the proportions of nonsmokers and smokers, respectively, who would say yes to this question. Given that y1 = 351 nonsmokers and y2 = 41 smokers said yes,

a. At the 5% level of significance, is there sufficient evidence that the proportion of adult Americans that favor this tax differs between smokers and nonsmokers?

b. Compute a 95% confidence interval for 1 – 2. Is this in agreement with the conclusion in part (a)? Explain.

a. At the 5% level of significance, is there sufficient evidence that the proportion of adult Americans that favor this tax differs between smokers and nonsmokers?

b. Compute a 95% confidence interval for 1 – 2. Is this in agreement with the conclusion in part (a)? Explain.

a. At the 5% level of significance, is there sufficient evidence that the proportion of adult Americans that favor this tax differs between smokers and nonsmokers?

b. Compute a 95% confidence interval for 1 – 2. Is this in agreement with the conclusion in part (a)? Explain.

Formulating the hypotheses
Ho: p1 - p2   =   0
Ha: p1 - p2   =/=   0
Here, we see that pdo =    0   , the hypothesized population proportion difference.

Getting p1^ and p2^,

p1^ = x1/n1 = 351/605 =    0.580165289
p2 = x2/n2 = 41/(800-605) =    0.21025641

Also, the standard error of the difference is

sd = sqrt[ p1 (1 - p1) / n1 + p2 (1 - p2) / n2] =    0.035413732

Thus,

z = [p1 - p2 - pdo]/sd =    10.44535149

As significance level =    0.05   , then the critical z is

zcrit =    1.959963985

Also, the p value is

P =    1.53884*10^-25

As P < 0.05, then we    REJECT THE NULL HYPOTHESIS.

Thus, there is significant difference between the proportion of adult Americans that favor this tax differs between smokers and nonsmokers. [CONCLUSION]

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For the   95%   confidence level, then

alpha/2 = (1 - confidence level)/2 =    0.025
z(alpha/2) =    1.959963985

lower bound = p1^ - p2^ - z(alpha/2) * sd =    0.30049924
upper bound = p1^ - p2^ + z(alpha/2) * sd =    0.439318518

Thus, the confidence interval is

(   0.30049924   ,   0.439318518 )

As this whole interval is greater than 0, then this is in agreement with part a.

There is a significant difference between the proportion of adult Americans that favor this tax differs between smokers and nonsmokers. [CONCLUSION]

Time, April 18, 1994, reported the results of a telephone poll of 800 adult Americans, 605 of them nonsmokers, who were asked the following question: “Should t

Time April 18 1994 reported the results of a telephone poll

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