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?

Answers: 1

Show answers

Answers

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

24 units

step-by-step explanation:

The graph of rectangle abcd is shown above

Answer from: Quest

A) for the n row: 22+(n-1)×6therefore,b) 100-22=78that means (n-1)×6=7878÷6=1313+1=1414th row has 100 seats

Another question on Mathematics

Mathematics, 21.06.2019 16:00

Arectangle with an area of 47 m² is dilated by a factor of 7. what is the area of the dilated rectangle? enter your answer in the box. do not leave your answer as a fraction.

Answers: 1

Answer

Mathematics, 21.06.2019 16:10

The box plot shows the number of raisins found in sample boxes from brand c and from brand d. each box weighs the same. what could you infer by comparing the range of the data for each brand? a) a box of raisins from either brand has about 28 raisins. b) the number of raisins in boxes from brand c varies more than boxes from brand d. c) the number of raisins in boxes from brand d varies more than boxes from brand c. d) the number of raisins in boxes from either brand varies about the same.

Answers: 2

Answer

Mathematics, 21.06.2019 20:00

What effect would doubling all the dimensions of a triangular pyramid have on the volume of the pyramid? explain your reasoning.

Answers: 1

Answer

Mathematics, 21.06.2019 20:10

Right triangle xyz has a right angle at vertex y and a hypotenuse that measures 24 cm. angle zxy measures 70º. what is the length of line segment xy? round to the nearest tenth. 8.2 cm 8.7 cm 22.6 m 25.5 cm

Answers: 1

Answer

You know the right answer?

Time magazine reported the result of a telephone poll of randomly selected adult Americans. The poll...

Questions

Mathematics, 01.02.2021 14:50

Find the value of:a) (3-¹+4-¹+5-¹)0this 0 at last is power.....