Question

A recent media source reported that 48% of eligible Alabamians are vaccinated against COVID 19. In order to test this claim, a local reporter gathered a random sample of 100 Alabamians and asked if they were vaccinated. What is the mean of our sampling distribution?

Answer 1

The mean of the sampling distribution, also known as the expected value, is an estimate of the population parameter (in this case, the proportion of eligible Alabamians who are vaccinated against COVID-19).

If the reporter gathered a random sample of 100 Alabamians and found that 48% of them were vaccinated, then the mean of the sampling distribution can be calculated as follows:

Mean = Sample Proportion

Mean = 48% = 0.48 (expressed as a decimal)

So, the mean of your sampling distribution is 0.48 or 48%. This means that based on your sample of 100 Alabamians, you estimate that 48% of eligible Alabamians are vaccinated against COVID-19. Keep in mind that this is just an estimate, and the true proportion in the entire population may be different.

Explanation: