For a population with $$ \sigma=10 $$ an $$ x $$ calculated from a sample of 36 observations will have a standarderror = (Round to two decimals)

Question

UpStudy AI · Accepted Answer

To calculate the standard error (SE) of the sample mean ($$ \bar{x} $$), we can use the formula:

$$
SE = \frac{\sigma}{\sqrt{n}}
$$

where:
- $$ \sigma $$ is the population standard deviation,
- $$ n $$ is the sample size.

Given:
- $$ \sigma = 10 $$
- $$ n = 36 $$

Now, we can substitute the values into the formula:

$$
SE = \frac{10}{\sqrt{36}}
$$

Calculating $$ \sqrt{36} $$:

$$
\sqrt{36} = 6
$$

Now substituting back into the SE formula:

$$
SE = \frac{10}{6}
$$

Calculating the final value:

$$
SE = 1.6667
$$

Rounding to two decimal places, we get:

$$
SE \approx 1.67
$$

Thus, the standard error is $$ 1.67 $$.
The standard error is 1.67.

For a population with \( \sigma=10 \) an \( x \) calculated from a sample of 36 observations will have a standarderror = (Round to two decimals)