1. Ch 5: Hypothesis Tests With Means of Samples Pt 3: Sept. 17, 2013

2. Confidence Intervals CI is alternative to a point estimate for an unknown population mean – Last week, we discussed how to calculate 95% and 99% CI (both 1 and 2-tailed). – Now, how to use these CI for hypothesis testing As an alternative to significance testing (the 5-step hypothesis testing procedure covered earlier in Ch 5) …a new example / review of how to calculate a CI…

3. Using CI for hypothesis testing Null & Research hypothesis developed same as for point estimate hyp test – Gather information needed: M (sample mean), N (sample size), μ (population mean), and σ (population SD) – Find σ M (standard dev of the distribution of means) – Find relevant z score(s) – based on 95 or 99% and 1-or 2- tailed test – Use z-to-x conversion formula for both positive and negative z values found in previous step (x = z(σ M ) + M) – This gives you the range of scores for the CI

4. – If the CI does not contain the mean from the null hyp (which is μ),  Reject Null. Note that the CI is built around M, so you don’t want to use M to make this comparison with the CI, but use μ (population comparison mean) So if μ is outside the interval, you conclude M and μ differ – Just like ‘rejecting the null’  we conclude the two means differ significantly

5. Point Estimate Hypothesis Testing (review) Is our decision based on the CI the same as we would make from the point estimate hypothesis test? – 1) Null & Research – 2 &3) Comparison Dist & Cutoff scores – 4) Find sample’s z score Z = (M - µ) / σ M – 5) Reject or fail to reject?