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

question 4

Short Answer

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 $n > 30$ .

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