Question

Time magazine reported the result of a telephone poll of 800 adult Americans. The question posed of the Americans who were surveyed was: ""Should the federal tax on cigarettes be raised to pay for health care reform?"" The results of the survey were: Non-smokers Smokers nN= 605 nS= 195 xN= 351 said yes xS= 41 said yes We wish to test if the proportions of people saying yes for the two groups are significantly different. a. State the null and alternative hypotheses. b. Conduct a two sample proportion test. Draw a conclusion using α = 0.01.

Answer 1

The observed value of z (test statistic) is greater than 1.96 (the test statistic does fall into the rejection region), so Reject H₀ .

p₁ = the proportion of the non-smoker population who reply "yes"

p₂ = the proportion of the smoker population who reply "yes," then we are interested in testing the null hypothesis

H₀:  p₁ = p₂

Alternate hypothesis:

Hₐ:  p₁≠p₂

That implies then that the test statistic for testing:

H₀ : p1 = p2

Hₐ : p1 ≠ p2.                              (Two – tailed)

n1 = 605, y1 = 351

p1 = y1 / n1

= 351/605

≈ 0.58

n2 = 195, y2 = 41.

p2 = y2/n2

= 41 / 195

≈0.21

p = y1 + y2 / n1 + n2

= 351 + 41 / 605 + 195

= 392 / 800

= 0.49

The test statistic is

$z = \frac{p1 - p2}{\sqrt{p(1-p). (\frac{1}{n1}}+ \frac{1}{n2} ) } }$

z = $\frac{0.58 - 0.21}\sqrt{{0.49 . 0.51 (\frac{1}{605} + \frac{1}{195} )} }$    

= 8.988

critical region for α = 0.01

z = 2.576

The observed value of z (test statistic) is greater than 1.96 (the test statistic does fall into the rejection region),

so Reject H₀ .

To learn more about hypothesis testing from the given link

brainly.com/question/4232174

#SPJ4