We know that a survey was conducted to analyze how many hours of television U.S teenagers watch each night. We also know that the sample mean (x) of the random sample of U.S. teenagers is 3 hours per night. We will consider how confident we are that the average of all U.S. teenagers (μ) is exactly 3 hours per night.
x = 3 ? ⟶ μ = 3
To do so let's recall the definitions of a population mean and a sample mean.
Population Mean (μ)
Mean of the all population
Sample Mean (x)
Mean of the sample data drawn from a population
A sample is a subset of a population. When collecting the population data is difficult, a sample data is used to make estimations about the population data. Moreover, to find the exact value we need to find the population mean. That is, we need to add all teenagers' screen times per night and divide it by the number of all U.S. teenagers.
μ=Sum of television times per night/Number of U.S teenagers
Collecting data from all U.S. teenagers is difficult, so a sample is selected for the survey. In this case, the margin of error E helps us to find the maximum difference between the sample mean and the population mean.
Consequently, by using the data of a sample we cannot expect that the average of all U.S teenagers is exactly 3 hours per night. However, the result might be close to 3 hours.
