What is the 95% confidence interval width for a sample with a mean of 50 and a standard deviation of 14 based on 75 observations?
A) (44.13, 55.87)
B) (46.83, 53.17)
C) (40.67, 59.32)
D) (48.22, 51.78)

Question

Quizplus · Accepted Answer

The 95% confidence interval is calculated as:
mean ± (1.96 x standard error)
where the standard error is calculated as:
standard deviation / sqrt(sample size)
Substituting the given values:
standard error = 14 / sqrt(75) = 1.613
95% confidence interval = 50 ± (1.96 x 1.613) = (46.83, 53.17)
Therefore, the width of the confidence interval is 53.17 - 46.83 = 6.34, which corresponds to answer choice B.

What Is the 95% Confidence Interval Width for a Sample