Assuming that all necessary conditions are met, what needs to be changed in the formula $\left( \bar { x } _ { 1 } - \bar { x } _ { 2 } \right) \pm z _ { \mathbb { \alpha } / 2 } \sqrt { S _ { p } ^ { 2 } \left( \frac { 1 } { n _ { 1 } } + \frac { 1 } { n _ { 2 } } \right) }$ so that we can use it to construct a confidence interval estimate for the difference of two population means when the population variances are assumed to be equal?
A) The $\bar { x } _ { 1 } - \bar { x } _ { 2 }$ should be replaced by $\mu _ { 1 } - \mu _ { 2 }$ .
B) The z $\alpha / 2$ should be replaced by $Z _ { \alpha }$ .
C) The z $\alpha / 2$ should be replaced by $t _ { \alpha / 2 }$ .
D) The $S _ { p } ^ { 2 }$ should be replaced by $s _ { 1 } ^ { 2 } + s _ { 2 } ^ { 2 }$ .

Question

Assuming that all necessary conditions are met, what needs to be changed in the formula $\left( \bar { x } _ { 1 } - \bar { x } _ { 2 } \right) \pm z _ { \mathbb { \alpha } / 2 } \sqrt { S _ { p } ^ { 2 } \left( \frac { 1 } { n _ { 1 } } + \frac { 1 } { n _ { 2 } } \right) }$ so that we can use it to construct a confidence interval estimate for the difference of two population means when the population variances are assumed to be equal?
A) The $\bar { x } _ { 1 } - \bar { x } _ { 2 }$ should be replaced by $\mu _ { 1 } - \mu _ { 2 }$ .
B) The z $\alpha  / 2$ should be replaced by $Z _ { \alpha }$ .
C) The z $\alpha / 2$ should be replaced by $t _ { \alpha / 2 }$ .
D) The $S _ { p } ^ { 2 }$ should be replaced by $s _ { 1 } ^ { 2 } + s _ { 2 } ^ { 2 }$ .

Quizplus · Accepted Answer

In order to construct a confidence interval estimate for the difference of two population means when the population variances are assumed to be equal, we need to use the t-distribution instead of the standard normal distribution. Therefore, the z $\alpha / 2$ should be replaced by $t _ { \alpha / 2 }$.

Assuming That All Necessary Conditions Are Met, What Needs to Be