169860
AssignmentMultiple Choice

Sampling Distribution of the Sample Mean

Question 169860 • NC-Math 4

Interpret the standard deviation of the sampling distribution of the sample mean.

Answer
A
The number of children per household is between 2.91 and 3.29 children for all households in the US.
B
The number of children per household is accurate 19% of the time.
C
In simple random samples of size 40, the sample mean number of children per household will typically vary by about 0.19 children from the true mean of 3.1 children.
D
In simple random samples of size 40, the sample mean number of children per household will always vary by precisely 0.19 children from the true mean of 3.1 children.

Explanation

The standard deviation of the sampling distribution describes the typical distance between sample means and the true population mean. Here, it is 0.19 children, so sample means from simple random samples of 40 households will typically differ from the true mean of 3.1 by about 0.19 children. It does not mean every sample differs by exactly 0.19, as choice D claims.

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