Ch 5: Hypothesis Tests With Means of Samples

Pt 3: Sept. 11, 2014

Confidence Intervals• CI is alternative to a point estimate for an

unknown population mean– In pt 2, 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 σM (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(σM) + 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) / σM

– 5) Reject or fail to reject?