Question

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??

Answer #1

Ans. For first population, to calculate the margin of error for 90% confidence interval, z distribution will be used.

For the second population, to calculate the margin of error for 90% confidence interval, student's t distribution will be used.

Although if the sample size is greater than 40 i.e. for sufficiently large samples student's t distribution can be approximated to z distribution.

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