The central limit theorem states that a. the sampling distribution of $\frac { \bar { Y } - \mu _ { Y } } { \sigma _ { \bar { Y } } }$ is approximately normal.
b. $\bar { Y } \stackrel { p } { \rightarrow } \mu _ { Y }$.
c. the probability that $\bar { Y }$ is in the range $\mu _ { Y } \pm c$ becomes arbitrarily close to one as $n$ increases for any constant $c 0$.
d. the $t$ distribution converges to the $F$ distribution for approximately $n 30$.

Question

The central limit theorem states that a. the sampling distribution of $\frac { \bar { Y } - \mu _ { Y } } { \sigma _ { \bar { Y } } }$ is approximately normal.
b. $\bar { Y } \stackrel { p } { \rightarrow } \mu _ { Y }$.
c. the probability that $\bar { Y }$ is in the range $\mu _ { Y } \pm c$ becomes arbitrarily close to one as $n$ increases for any constant $c > 0$.
d. the $t$ distribution converges to the $F$ distribution for approximately $n > 30$.

Quizplus · Accepted Answer

The Answer of The central limit theorem states that a. the sampling distribution of $\frac { \bar { Y } - \mu _ { Y } } { \sigma _ { \bar { Y } } }$ is approximately normal.
b. $\bar { Y } \stackrel { p } { \rightarrow } \mu _ { Y }$.
c. the probability that $\bar { Y }$ is in the range $\mu _ { Y } \pm c$ becomes arbitrarily close to one as $n$ increases for any constant $c > 0$.
d. the $t$ distribution converges to the $F$ distribution for approximately $n > 30$.

The Central Limit Theorem States That A Yˉ−μYσYˉ\frac { \bar { Y } - \mu _ { Y } } { \sigma _ { \bar { Y } } }σYˉ​Yˉ−μY​​

The Central Limit Theorem States That A $\frac { \bar { Y } - \mu _ { Y } } { \sigma _ { \bar { Y } } }$