- 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?
- for an estimation problem, list two ways of reducing the magnitude of sampling error?
- 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.
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The usual rule that is applied in this situation is to use the normal distribution if the sample size is 30 or more.
The sampling error is sigma/sqrt(n) and thus to reduce the sampling error you need to decrease sigma or increase n.
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.