The heights of a random sample of 100 women are recorded. The sample mean is 65.3 inches and the sample standard deviation is 3 inches. Which of the following is an approximate 95% confidence interval for the population mean?

Question

Quizplus · Accepted Answer

The correct formula for a 95% confidence interval is the sample mean $\pm$ the margin of error, where the margin of error is calculated as the critical value (approximately 2 for 95% confidence) times the standard error of the mean. The standard error of the mean is the sample standard deviation divided by the square root of the sample size. Given a sample standard deviation of 3 inches and a sample size of 100, the standard error is $3/\sqrt{100} = 3/10 = 0.3$. Therefore, the margin of error is $2 \times 0.3$, making the correct choice 65.3 $\pm$ (2)(0.3).

The Heights of a Random Sample of 100 Women Are ±\pm±

The Heights of a Random Sample of 100 Women Are $\pm$