Lab Chapter 9: Confidence Interval E370 Spring 2013

What’s CI? Why do we need it? The purpose of statistics: use sample mean/proportion to estimate parameters. We do not know how close are the point estimates (sample mean/proportion) to the true value (population mean/proportion.) Hence, we want to construct an interval by the sample mean/proportion and ask, what is the probability that this random interval will contain the population mean/proportion.

Construct Confidence Interval for Population Mean (true value) When population SD(σ) is known : use normal distribution SE Z-value

Construct Confidence Interval for Population Mean When population SD(σ) is unknown : use t-distribution SE t-value

Construct Confidence Interval for Population Proportion “p” (Never use “t-score”!) When and : (CHECK!!) SE Z-value

When Margin of Error (e) is Given, To Decide The Sample Size : (Round “n” into the NEXT whole number)

Steps to Construct a Confidence Interval Step 1: Choose α: (1-α) is your level of confidence. α is the probability that any CI ( constructed form the same size random sample from the population) will not contain the parameter. Step 2: Calculate the appropriate point estimate: Sample mean or sample proportion. Step 3: Calculate the margin of error. Step 4: Add and subtract the margin of error to and from the point estimate: CI is (Point estimate ± margin of error).