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# 尋求統計學高手解題

9. The following data give the number of pets owned for a population of 4

families

Family A B C D

Number of Pets Owned2 1 4 3

Samples of size 2 will be drawn at random from the population

(without replacement).

(1) Find the mean of the sampling distribution of the sample means.

(2) Find the standard deviation of the sampling distribution of the sample

means.

(3) Find the sampling distribution of X , and use it directly to recalculate the

mean and the standard deviation of X .

### 1 Answer

- Go_BadgersLv 71 decade agoFavorite Answer
The following data give the number of pets owned for a population of 4

families

Family A B C D

Number of Pets Owned：2 1 4 3

Samples of size 2 will be drawn at random from the population

(without replacement).

母體的平均數為2.5，變異數為1.25，標準差為1.118034。

(1) Find the mean of the sampling distribution of the sample means.

有4*3=12種可能抽樣。樣本平均數的均值為2.5。

(2) Find the standard deviation of the sampling distribution of the sample means.

樣本平均數的標準差為[√(4-2)/(4-1)] * 1.118034/√2 = 0.6455。

(3) Find the sampling distribution of X , and use it directly to recalculate the mean and the standard deviation of X .

P(X_bar=1.5) = 1/6

P(X_bar=2) = 1/6

P(X_bar=2.5) = 2/6

P(X_bar=3) = 1/6

P(X_bar=3.5) = 1/6

mean = 1.5*(1/6)+2*(1/6)+2.5*(2/6)+3*(1/6)+3.5*(1/6) = 2.5

variance = (1.5-2.5)2 *(1/6) + (2-2.5)2 *(1/6) + (2.5-2.5)2 *(2/6) + (3-2.5)2 *(1/6) + (3.5-2.5)2 *(1/6) = 0.4167

standard deviation = √0.4167 = 0.6455

Same answers as above in (1) and (2)！