Question

The tobacco industry closely monitors all surveys that involve smoking. One survey showed that among 785 randomly selected subjects who completed 4 years of college, 18.3% smoke (based on data from American Medical Association). The 99% confidence interval for the true percentage of smokers of all people who completed 4 years of college is closest to (a) (0.160, 0.206) (e) (0.138, 0.228) (b) (0.165, 0.201) (c) (0.156, 0.210)(d) (0.147, 0.219)

Answer 1

To calculate the 99% confidence interval for the true percentage of smokers of all people who completed 4 years of college, we can use a formula that incorporates the observed percentage, sample size, and the z-score for the desired confidence level. Plugging in the given values, the confidence interval is approximately (0.160, 0.206).

Step-by-step explanation:

To calculate the 99% confidence interval for the true percentage of smokers of all people who completed 4 years of college, we can use the formula:

CI = p ± Z * sqrt(p * (1-p)/n)

Where:

• CI is the confidence interval
• p is the observed percentage of smokers (18.3%, or 0.183)
• Z is the z-score corresponding to the desired confidence level (for 99% confidence, Z is approximately 2.576)
• n is the sample size (785)

Plugging in the values, we get:

CI = 0.183 ± 2.576 * sqrt(0.183 * (1-0.183)/785)

Simplifying, the confidence interval is approximately (0.160, 0.206).