Question

Based on a random sample of 120 students, a 95% confidence interval for the proportion of students that have a job is (0.67, 0.83). Which of the following is true?

A. 95 of the sampled students have a job.

B. the margin of error for the confidence interval is 0.16.

C. a larger sample size would yield a wider confidence interval.

D. if we used a different confidence level, the interval would not be symmetric about the sample proportion.

E. none of these are true.

Answer 1

The correct interpretation of the given 95% confidence interval (0.67, 0.83) is that the margin of error is 0.16. This is calculated by subtracting the lower limit from the upper limit of the confidence interval.

Step-by-step explanation:

Among the given options, the correct interpretation of the 95% confidence interval for the proportion of students that have a job, which is (0.67, 0.83), is that the margin of error for the confidence interval is 0.16. Here's why:

• The confidence interval does not tell us that 95 of the sampled students have a job. It provides an estimate of the true proportion of the entire population of students who have a job.
• The margin of error is calculated as the value above or below the sample proportion that the actual population proportion is expected to be within a certain confidence level. In this case, it is indeed 0.16 (0.83 - 0.67).
• A larger sample size would not yield a wider confidence interval. In fact, it generally results in a narrower confidence interval, assuming the variability in the population does not change.
• If we used a different confidence level, while the confidence interval might be wider or narrower, it is generally symmetric about the sample proportion provided the sample size is sufficiently large and the sample proportion is not close to 0 or 1.

Therefore, the correct answer is B: the margin of error for the confidence interval is 0.16.