1. given: n = 40, standard deviation is not known, population of individual observations not normal. does the central limit theorem apply in this case? why or why not?

  2. for an estimation problem, list two ways of reducing the magnitude of sampling error?

  3. What will happen to the magnitude of sampling error if the confidence level is raised all other things remaining the same? justify your answer?

thank you for your help.


  1. The usual rule that is applied in this situation is to use the normal distribution if the sample size is 30 or more.

  2. The sampling error is sigma/sqrt(n) and thus to reduce the sampling error you need to decrease sigma or increase n.

  3. In this case I am assuming that the sampling error is the width of the confidence interval. If you raise the confidence level, say from 95% to 99% then the width of the confidence interval will increase. Look at the expression for the confidence interval and see what happens as you increase the confidence level.

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