In the formula $\bar { x } \pm z _ { \alpha / 2 } ( ?/ \sqrt { n } )$
,the subscript $( \alpha / 2 )$ refers to the:
A) probability that the confidence interval will contain the population mean.
B) probability that the confidence interval will not contain the population mean.
C) area in the lower tail or upper tail of the sampling distribution of the sample mean.
D) level of confidence.
E) sampling error.

Question

In the formula $\bar { x } \pm z _ { \alpha / 2 } ( ?/ \sqrt { n } )$
 ,the subscript $( \alpha / 2 )$ refers to the:
A) probability that the confidence interval will contain the population mean.
B) probability that the confidence interval will not contain the population mean.
C) area in the lower tail or upper tail of the sampling distribution of the sample mean.
D) level of confidence.
E) sampling error.

Quizplus · Accepted Answer

The subscript $(\alpha/2)$ refers to the area in the lower tail or upper tail of the sampling distribution of the sample mean. This area represents the probability of observing a certain value of the sample mean if we assume that the null hypothesis (in this case, that the true population mean is equal to the sample mean) is true. By choosing a specific value of $\alpha$ (typically 0.05 or 0.01), we can determine the corresponding value of $z_{\alpha / 2}$ that will give us the desired level of confidence in our confidence interval.

In the Formula xˉ±zα/2(?/n)\bar { x } \pm z _ { \alpha / 2 } ( ?/ \sqrt { n } )xˉ±zα/2​(?/n​)

In the Formula $\bar { x } \pm z _ { \alpha / 2 } ( ?/ \sqrt { n } )$