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Moderate

Sampling Distribution of a Sample Mean: Homeytown

APSTAT-LKGL1O

A survey conducted in Homeytown found that the average number of people per household was $4.3$ with a standard deviation of $1.2$. The true average size and standard deviation of a household in Homeytown is $4.1$ and $0.98$ respectively.

Using simple random samples of size $50$, what are the mean and standard deviation for the sampling distribution of the sample means of the number of people per household in Homeytown?

A

$4.1,\cfrac { 0.98 }{ \sqrt { 50 } } $

B

$4.1,\cfrac { 1.12 }{ \sqrt { 50 } } $

C

$4.1, 0.98$

D

$4.3,\cfrac { 1.12 }{ \sqrt { 50 } } $

E

$4,3, 1.12$