Question

3) In 2005, 21% of Americans reported that they smoked cigarettes. In a recent study to see if the percentage has changed since 2005, researchers surveyed 2000 Americans where 380 of them responded to the survey as smokers. Does the evidence provided by the recent survey appear to support the claim that the percent of Americans who smoke has changed since 2005 at the 5% significance level? (Circle either Yes or No). YES NO Please show the four steps of your analysis in the space provided below...

Answer 1

Answer 3: In 2005, 21% of Americans reported that they smoked cigarettes. In a recent study to see if the percentage has changed since 2005, researchers surveyed 2000 Americans where 380 of them responded to the survey as smokers. Does the evidence provided by the recent survey appear to support the claims that the percent of americans who smoke has changed since 2005 at the 5% significant level.

Solution:

p = 21% = 0.21

x = 380

n = 2000

p̂ = x/n

p̂ = 380/2000

p̂ = 0.19

The hypothesis test:

Ho: p = 0.21

Ha: p ≠ 0.21

Test statistic Z:

Z = p̂ - p / √p(1-p)/n

Z = 0.19 - 0.21 / √0.21(1 - 0.21)/2000

Z = -2.1959

Test statistic Z = - 2.196

P-value from test statistic Z at α = 0.05:

P-Value = 0.0281.

Since, P-value (0.0281) < α (0.05) significance level.

We reject the null hypothesis Ho.

Conclusion:

Reject Ho. Yes, there is sufficient evidence to support the claims that the percent of americans who smoke has changed since 2005 at the 5% significant level.