Question

Among 1815 randomly selected high school students surveyed by the Centers for Disease Control, 417 said they were current smokers. What is the 95% confidence interval? (Round to three decimal places.)

A. [0.212, 0.253]
B. [0.227, 0.272]
C. [0.188, 0.226]
D. [0.267, 0.312]

Answer 1

To find the 95% confidence interval for the proportion of smokers among the surveyed students, we use the standard formula with the sample proportion, z-score for 95% confidence, and the sample size. After the calculations, the correct confidence interval is option B. [0.227, 0.272].

Step-by-step explanation:

To find the 95% confidence interval for the proportion of high school students who are current smokers, based on the survey results, we'll use the standard formula for a confidence interval for a population proportion.

The formula for a confidence interval is:

P +- z * sqrt((P(1-P))/n)

Where P is the sample proportion, z is the z-score corresponding to the confidence level (in this case, for 95%, z is approximately 1.96), and n is the sample size.

We're given that out of 1815 students, 417 are current smokers. So, P = 417/1815.

The calculation steps will be:

1. Calculate the sample proportion (P).
2. Find the z-score for a 95% confidence level (z = 1.96).
3. Calculate the standard error (SE = sqrt((P(1-P))/n)).
4. Compute the confidence interval using P +- z * SE.

After performing these calculations, the correct interval would be option B. [0.227, 0.272].