Which of the following statements are true?
A) The interval $\bar { X } \pm 1.96 \cdot \sigma/ \sqrt { n }$
Is random, while its width is not random.
B) The interval $\bar { X } \pm 1.96 \cdot \sigma / \sqrt { n }$
Is not random, while its width is random.
C) The interval $\bar { x } \pm 1.96 \cdot \sigma / \sqrt { n }$
Is random, while its width is not random.
D) The interval $\bar { x } \pm 1.96 \cdot \sigma / \sqrt { n }$
Is not random, while its width is random.
E) None of the above statements are true.

Question

Quizplus · Accepted Answer

CThe intervals given in both A and C are confidence intervals for the mean, which are random because they are based on the sample mean ($\bar{X}$ or $\bar{x}$), which varies from sample to sample. However, the width of these intervals is not random because it is determined by the fixed value 1.96 (which comes from the standard normal distribution for a 95% confidence level), the population standard deviation ($\sigma$), and the sample size ($n$), none of which are random once the sample is taken.

Which of the Following Statements Are True? A) the Interval Xˉ±1.96⋅σ/n\bar { X } \pm 1.96 \cdot \sigma/ \sqrt { n }Xˉ±1.96⋅σ/n​

Which of the Following Statements Are True?
A) the Interval $\bar { X } \pm 1.96 \cdot \sigma/ \sqrt { n }$