Question

6. The actual population mean rating of all 100 computer games is 7.5. Does your class distribution of sample means center at 7.5? Discuss why it does or does not.

Answer 1

False. Not always we expect this. See explanation below.

Explanation:

If we assume that we play a game 100 times and on each game we have k results, we can calculate the sum of the k results and divide by 100 and we got the sample mean for this case.

In theory we have this:

`\bar X = (\sum_(i=1)^n X_i)/(n)`

And the expected value for the sample mean is:

`E(\bar X) = (1)/(n) \sum_(i=1)^n E(X_i) = \mu`

But in practice this result is not satisfied always since if we use random numbers generated by a computer for example we don't know if the generator is using any method that gives more probability to some numbers on specific or any other problems related to the generation of the numbers.

So then not always we expect this result. A possible reason why their sample means do not center at 7.5 is that we probably need more samples in order to have less bias about the estimation.

So then if we use a random generator number They may suggest that they were very improbable that we will get a distribution centered at 7.5. It can happen, but it is not likely.