Question

The American Heart Association is about to conduct an anti-smoking campaign and wants to know the fraction of Americans over 36 who smoke. Step 1 of 2: Suppose a sample of 632 Americans over 36 is drawn. Of these people, 430 430 don't smoke. Using the data, estimate the proportion of Americans over 36 36 who smoke. Enter your answer as a fraction or a decimal number rounded to three decimal places then calculate lower and upper endpoints

Answer 1

Solution :

Given that,

n = 632

430 don't smoke

smoke = 632 - 430 = 202

x = 202

Point estimate = sample proportion = = x / n = 202 / 632 = 0.320

1 - = 1 - 0.320 = 0.680

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z_/2 = Z_0.025 = 1.96

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

= 1.96 * (((0.320 * 0.680) / 632)

= 0.037

A 95% confidence interval for population proportion p is ,

- E < p < + E

0.320 - 0.037 < p < 0.320 + 0.037

0.283 < p < 0.357

Lower endpoint = 0.283

Upper endpoint = 0.357