For the interval estimation of μ when σ is known and the sample is large, the proper distribution to use is the
A) normal distribution.
B) t distribution with n degrees of freedom.
C) t distribution with n + 1 degrees of freedom.
D) t distribution with n - 1 degrees of freedom.

Question

Quizplus · Accepted Answer

When σ is known and the sample size is large (n>30), we use the normal distribution for interval estimation of the population mean (μ). The central limit theorem states that the sample mean will be approximately normally distributed regardless of the distribution of the population from which the sample was drawn, provided the sample size is sufficiently large. Therefore, the normal distribution is the most appropriate choice for interval estimation in this case.

For the Interval Estimation of μ When σ Is Known