Consider a normally distributed population with unknown standard deviation.When computing a confidence interval for the population mean,the values $t _ { \alpha / 2 }$
And $z _ { \alpha / 2 }$
Will be close in value when
A)the sample size is small.
B)the sample size is large.
C)the sample mean is small.
D)the sample mean is large.
E)the sample standard deviation is small.

Question

Quizplus · Accepted Answer

When the sample size is large, the t-distribution approaches the normal distribution, making $t _ { \alpha / 2 }$ and $z _ { \alpha / 2 }$ values close in value due to the central limit theorem.

Consider a Normally Distributed Population with Unknown Standard Deviation tα/2t _ { \alpha / 2 }tα/2​

Consider a Normally Distributed Population with Unknown Standard Deviation $t _ { \alpha / 2 }$