The purpose of this assignment is to understand the role of margin of error in constructing confidence interval when population standard deviation () is known and unknown.

1. Develop 90 %, 95 %, and 99% confidence intervals for population mean () when sample mean is 10 with the sample size of 100. Population standard deviation is known to be 5.
2. Suppose that sample size changes to 144 and 225. Develop three confidence intervals again. What happens to the margin of error when sample size increases?
3. A simple random sample of 400 individuals provides 100 yes responses. Compute the 90%, 95%, and 99% confidence interval for population proportion (p).
4. With the same random sample as in 3, if the sample size increases to 1000, what happens to the three confidence intervals?

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