Mathematics, 21.04.2020 02:26 sainijasdeep27

Time magazine reported the result of a telephone poll of randomly selected adult Americans. The poll asked these adult Americans: "Should the federal tax on cigarettes be raised to pay for health care reform?" The results of the survey showed that among 620 non-smokers, 318 had said "yes" and among 195 smokers, 35 had said "yes".
We want to estimate the actual difference between the proportions of non-smokers and smokers who said "yes" to federal tax increase. Notation: 1=non-smokers and 2-smokers. Based on this data, what is the upper bound for a 95% confidence interval for the difference in the population proportions, Pi - P2?

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Answer from: pthalia

The 95% confidence interval for the difference in the population proportions( Pi - P2)

(0.2674 ,0.4055)

the upper bound for a 95% confidence interval for the difference in the population proportions, Pi - P2

0.4055

Step-by-step explanation:

Step :- (1)

Given data the results of the survey showed that among 620 non-smokers, 318 had said "yes"

The first proportion $p_{1} = \frac{318}{620} =0.5129$

q₁ = 1- p₁ = 1-0.5129 =0.4871

Given data the results of the survey showed that among 195 smokers, 35 had said "yes".

The second proportion $p_{2} = \frac{35}{195} =0.179$

q₂ = 1- p₂ = 1-0.179 =0.821

Step :-(2)

The 95% confidence interval for the difference in the population proportions( Pi - P2)

(p₁-p₂ ± z₀.₉₅ se(p₁-p₂))

The standard error (p₁-p₂) is defined by

= $\sqrt{\frac{p_{1}q_{1} }{n_{1} }+\frac{p_{2}q_{2} }{n_{2} } }$

= $\sqrt{\frac{0.5129 X 0.4871 }{620 }+\frac{0.179 X 0.821 }{195 } }$

= 0.0339

The 95% confidence interval for the difference in the population proportions( Pi - P2)

(p₁-p₂ ± z₀.₉₅ se(p₁-p₂))

(p₁-p₂ - z₀.₉₅ se(p₁-p₂) , p₁-p₂ + z₀.₉₅ se(p₁-p₂) )

(0.5129-0.179) - 1.96 × 0.0339 , 0.5129 -0.179) - 1.96 × 0.0339)

(0.339 -0.0665 , 0.339 +0.0665 )

(0.2674 ,0.4055)

Conclusion:-

The 95% confidence interval for the difference in the population proportions( Pi - P2)

(0.2674 ,0.4055)

Answer from: cuhh

The 95% confidence interval for difference in proportion of non-smokers and smokers who said "yes" to federal tax increase is (0.26, 0.40).

Step-by-step explanation:

The confidence interval for difference in proportion formula is,

$CI=(\hat p_{1}-\hat p_{2})\pm z_{\alpha/2}\times \sqrt{\frac{\hat p_{1}(1-\hat p_{1})}{n_{1}}+\frac{\hat p_{2}(1-\hat p_{2})}{n_{2}}}$

The given information is:

$n_{1}=620\\n_{2}=195\\X_{1}=318\\X_{2}=35$

Compute the sample proportions as follows:

$\hat p_{1}=\frac{X_{1}}{n_{1}}=\frac{318}{620}=0.51\\\\\hat p_{2}=\frac{X_{2}}{n_{2}}=\frac{35}{195}=0.18$

Compute the critical value of z for the 95% confidence level as follows:

$z_{\alpha/2}=z_{0.05/2}=z_{0.025}=1.96$

*Use the standard normal table.

Compute the 95% confidence interval for difference between proportions as follows:

$CI=(\hat p_{1}-\hat p_{2})\pm z_{\alpha/2}\times \sqrt{\frac{\hat p_{1}(1-\hat p_{1})}{n_{1}}+\frac{\hat p_{2}(1-\hat p_{2})}{n_{2}}}$

$=(0.51-0.18)\pm 1.96\times \sqrt{\frac{0.51(1-0.51)}{620}+\frac{0.18(1-0.18)}{195}}$

$=0.33\pm 0.067\\=(0.263, 0.397)\\\approx (0.26, 0.40)$

Thus, the 95% confidence interval for difference in proportion of non-smokers and smokers who said "yes" to federal tax increase is (0.26, 0.40).

Answer from: Quest

the law of definite proportions states samples of a compound will always contain the same proportion of elements by mass. in other words, a given compound will always contain the same elements in the same proportions by mass.the law of multiple proportions states when two elements combine with each other to form more than one compound, then the weights of one element that combine with a fixed weight of the other are in a ratio of small whole numbers.

Answer from: Quest

113.42

i hope that is right.

step-by-step explanation:

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