Confidence Intervals Chapter 10 Section 1

Confidence Interval – an interval obtained from sample data that tries to estimate the true population mean. (It’s a range of plausible values for the parameter) It gives the probability that the method used will produce an interval that contains the true mean µ. is at its center and the level of confidence determines the length of its extending arms Note: remember any statistic can be substituted in where is for corresponding parameter.

Confidence interval for means ± z*(σ/√n) Estimate ± Margin of Error = sample mean σ = standard deviation of population z* = confidence level, called the upper critical value n = sample size Assumptions / Conditions: Independent observations Normal Distribution σ is known

Properties of Confidence Intervals As confidence goes up margin of error goes up and vice versa as confidence margin of error If there is a large variation in population (large σ) margin of error is large As sample size, n, the margin of error ,m,

Two ways to state your results: Interpreting Confidence Level. (90)% of all possible samples of the same size from this population give an interval that will capture the true population parameter (mean or proportion). Interpreting Confidence Interval: We are (90)% confident the interval will contain the true population parameter (mean). CANNOT SAY: the population mean, µ, will fall in this interval (90%) of the time Confidence Interval Simulation

Assignment: Pages: 512 & 513 problems 1 & 3 518 & 519 5 & 7 521 & 522 9 & 11