Question

A sample with a mean of m = 40 and a variance of s2 = 20 has an estimated standard error of 1 point. how many scores are in the sample? group of answer choices 4 5 20 21

Answer 1

The correct option is 20.

The score found for the sample is 20.

What is Standard error?

A standard error is a statistic that is applied to test the distribution of data. This metric is comparable to standard deviation. We can calculate the standard error if we know the sample size & standard deviation. It assesses the mean's precision.

Now, according to the question;

Sample mean; $\bar{x}=40$

Sample variance; $s^{2}=20$

Thus, $s=\sqrt{20}=4.47$

Standard error SE = 1

The amount of scores with in sample must be determined here.

The standard error formula is as follows:

$S E=\frac{s}{\sqrt{n}}$

We might rearrange the formula as follows:

$\begin{aligned}\sqrt{n} &=\frac{s}{S E} \\n &=\left(\frac{s}{S E}\right)^{2}\end{aligned}$

Substituting the values;

$\begin{aligned}&n=\left(\frac{4.47}{1}\right)^{2} \\&n=19.98\end{aligned}$

The sample's number of scores n = 19.98 = 20 (round up)

Therefore, the scores are in the sample is 20.

To know more about the Standard error, here

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