Question

The time spent on social media platforms per day by adults has a distribution with a mean of 120 minutes and a standard deviation of 36 minutes. A random sample of size 36 adults is selected from the population. Find the mean and standard error of the sample mean time spent on social media platforms per day.

Answer 1

The mean of the sample mean time spent on social media platforms per day is 120 minutes, and the standard error is 6 minutes.

Step-by-step explanation:

The mean time spent on social media platforms per day by adults is given as 120 minutes with a standard deviation of 36 minutes. Since a random sample of size 36 adults is selected, to find the mean and standard error of the sample mean time we use the following formulas:

Mean of the sample mean (also called the expected value of the sample mean) is the same as the population mean, which is 120 minutes.

Standard Error of the sample mean is calculated using the formula SE = σ/√n, where σ is the standard deviation of the population and n is the sample size.

In this case, SE = 36/√36 = 36/6 = 6 minutes.

Therefore, the mean of the sample mean is 120 minutes, and the standard error is 6 minutes.