Question

The American Heart Association is about to conduct an anti-smoking campaign and wants to know the fraction of Americans over 25 who smoke.

Step 1 of 2: Suppose a sample of 2017 Americans over 25 is drawn. Of these people, 564 smoke. Using the data, estimate the proportion of Americans over 25 who smoke. Enter your answer as a fraction or a decimal number rounded to three decimal places.

Step 2 of 2:

Suppose a sample of 2017 Americans over 25 is drawn. Of these people, 564 smoke. Using the data, construct the 95% confidence interval for the population proportion of Americans over 25 who smoke. Round your answers to three decimal places.

Answer 1

Solution :

Given that,

n = 564

x = 25

Point estimate = sample proportion = = x / n = 25/564=0.044

1 - = 1 - 0.044=0.956

At 95% confidence level

= 1 - 95%

=1 - 0.95 =0.05

/2 = 0.025

Z/2 = Z_{0.025 = 1.96}

Margin of error = E = Z _{/ 2} * (( * (1 - )) / n)

= 1.96 (((0.044*0.956) /564 )

= 0.017

A 95% confidence interval for population proportion p is ,

- E < p < + E

0.044 - 0.017 < p <0.044 + 0.017

0.027< p < 0.061

The 95% confidence interval for the population proportion p is :(0.027 ,  0.061)