Question

question 1 of 7
assume a recent sociological report states that college students drink 4.14 glasses of milk per week on average, with a standard deviation of 1.5301. suppose jason, the cafeteria manager at a local college, decides to take a random sample of 150 college students and ask them how many glasses of milk they typically drink in a week.
determine the mean and standard deviation of the sampling distribution of the sample mean milk consumption.
$mu_{\bar{x}} =$ _______ glasses of milk (round to 2 decimal places.)
$sigma_{\bar{x}} =$ _______ glasses of milk (round to 2 decimal places.)

Explanation:

Step1: Find sampling mean

The mean of the sampling distribution of the sample mean equals the population mean.
$\mu_{\bar{x}} = \mu = 4.14$

Step2: Calculate standard error

The standard deviation (standard error) of the sampling distribution is the population standard deviation divided by the square root of the sample size.
$\sigma_{\bar{x}} = \frac{\sigma}{\sqrt{n}} = \frac{1.5301}{\sqrt{150}}$
First, calculate $\sqrt{150} \approx 12.2474$, then $\frac{1.5301}{12.2474} \approx 0.125$
Round to 2 decimal places: $\sigma_{\bar{x}} \approx 0.13$

Answer:

$\mu_{\bar{x}} = 4.14$ glasses of milk
$\sigma_{\bar{x}} = 0.13$ glasses of milk