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

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…

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

– 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

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?