Math / Data & Statistics

QuestionDetermine $\mu_{\bar{x}}$ and $\sigma_{\bar{x}}$ from the given parameters of the population and sample size. $\begin{array}{l} \mu=76, \sigma=7, n=49 \\ \mu_{\bar{x}}=\square \end{array}$ $\square$

Studdy Solution

STEP 1

1. The population mean $\mu$ is given as 76.
2. The population standard deviation $\sigma$ is given as 7.
3. The sample size $n$ is 49.
4. $\mu_{\bar{x}}$ is the mean of the sampling distribution of the sample mean.
5. $\sigma_{\bar{x}}$ is the standard deviation of the sampling distribution of the sample mean.

STEP 2

1. Calculate $\mu_{\bar{x}}$ .
2. Calculate $\sigma_{\bar{x}}$ .

STEP 3

Calculate $\mu_{\bar{x}}$ .
The mean of the sampling distribution of the sample mean $\mu_{\bar{x}}$ is equal to the population mean $\mu$ .
$\mu_{\bar{x}} = \mu = 76$

STEP 4

Calculate $\sigma_{\bar{x}}$ .
The standard deviation of the sampling distribution of the sample mean $\sigma_{\bar{x}}$ is given by:
$\sigma_{\bar{x}} = \frac{\sigma}{\sqrt{n}}$
Substitute the given values:
$\sigma_{\bar{x}} = \frac{7}{\sqrt{49}} = \frac{7}{7} = 1$
The calculated values are:
$\mu_{\bar{x}} = 76, \quad \sigma_{\bar{x}} = 1$

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