Question

8- Suppose that you have two populations: - Population A: you do not know the distribution,...

8- Suppose that you have two populations: - Population A: you do not know the distribution, mean, and the variance of the population. - Population B: you do not know the distribution and the mean of the population. But you know the variance of the population. Now you want to build a %90 confidence level interval for the mean of each population separately by sampling. What is the difference between the methods you use for each population?

Homework Answers

Answer #1

Without loss of generality, if the sample size is sufficiently large, we can assume that the two populations are normally distributed.

Now, for population A, the mean and variance are unknown.

For population B, the mean is unknown but the variance is known.

Now, in order to construct the confidence interval for the mean of each population, we do know the variance for population B, but we do not know the variance for population A. We need to use the sample variance as an estimate of population variance in population A.

So, we have to build a confidence interval based on t-test (i.e. t-distribution should be used) for population A and based on z-test (i.e. standard normal distribution should be used) for Population B.

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