A random sample of size n=100 is taken

lungicibane794

lungicibane794

Answered question

2022-07-17

A random sample of size n=100 is taken from a population with mean u =80 and a standard deviation o=14.Calculate the expected value of the sample mean

Answer & Explanation

Eliza Beth13

Eliza Beth13

Skilled2023-05-31Added 130 answers

To calculate the expected value of the sample mean, we need to consider the properties of the sample mean and the population from which the sample is drawn.
The expected value, denoted as E(X¯), represents the average value we would expect to obtain if we repeatedly take samples from the population and calculate the mean of each sample.
We have a random sample of size n=100 taken from a population with a mean μ=80 and a standard deviation σ=14. The sample mean is calculated by taking the average of all the observations in the sample.
The expected value of the sample mean can be calculated using the formula:
E(X¯)=μ
where μ is the population mean. In other words, the expected value of the sample mean is equal to the population mean.
Substituting the given values into the formula, we have:
E(X¯)=80
Therefore, the expected value of the sample mean, based on a random sample of size n=100 taken from a population with mean μ=80 and standard deviation σ=14, is 80.

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