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Ch 5: Hypothesis Tests With Means of Samples

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

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Ch 5: Hypothesis Tests With Means of Samples

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  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 hyptest • 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

  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 μdiffer • 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) / σM • 5) Reject or fail to reject?

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