1. Matched pairs t procedures Section 11.1.3

2. Starter 11.1.3 Scores on the AP exam are supposed to have a mean of 3. Mr. McPeak thinks his students score higher than that, so he takes a sample of ten of last year’s scores Here are the scores: Using the methods we learned yesterday: –Find a 95% confidence interval for the mean from the formula –Perform a hypothesis test that might support Mr. McPeak’s claim Clearly state your conclusion in a sentence 22534 35414

3. Today’s Objectives Students will perform a matched-pairs t procedure Students will use the TI to calculate one-sample confidence intervals Students will use the TI to calculate one-sample t-tests California Standard 20.0 Students are familiar with the t distributions and t test and understand their uses.

4. Matched pairs t procedures Compare the before and after responses in a matched pairs experiment Use one-sample t procedures on the observed individual differences So H o is always μ = 0 Then H a is one of three choices: –μ ≠ 0 –μ > 0 –μ < 0

5. Example: Here are the scores for 12 golfers who played two rounds each on a new course. Perhaps course knowledge helps scores. Is there evidence that their scores improved (got lower) on the second round? (Put data in TI) GolferABCDEFGHIJKL First Round 89908795868110210583889179 Second Round 948589 81761078987918880

6. Example continued Find the difference (R 1 – R 2 ) for each player State the hypotheses: –H o : μ = 0 –H a : μ > 0 (Why not less than?) Find the mean and StdDev of the twelve differences

7. Solution concluded From 1-var stats: Ë= 1.67S=6.20n = 12 Calculate t: Calculate P: –tcdf(0.933, 999, 11) = 0.185 Write a conclusion –There is not sufficient evidence at any reasonable level of α (t 11 =0.933, P=.185) to support the claim that experience lowers scores

8. Hypothesis Tests on the TI Use Stat:Tests:T-Test Choose Data or Stats Set μ o = H o Choose appropriate H a Calculate Write a sentence that summarizes your conclusion

9. Example The golf coach claims her players will do better on the second round. Do the data support the claim? Form hypotheses Conduct the test on the TI Write your conclusion

10. Solution H o : μ = 0H a : μ > 0 On the T-Test screen, choose data and L 3, let μ o =0, μ>μ o Calculate to find t =.931, P =.186 Conclusion: Since P is high, there is not sufficient evidence to support the claim that course knowledge improves scores

11. Confidence Intervals on the TI Use the Stat:Tests:T-interval screen Choose Data or Stats –Data Enter list name and frequency (usually 1) –Stats Enter mean, StdDev and sample size Choose confidence level Calculate Clearly state your conclusion

12. Example Form a 95% C.I. for the mean golf score improvement –Remember your differences are in L 3 You should find (-2.272, 5.605) What does that say about whether scores improved? Since the confidence interval includes zero, this does not support an improvement in scores.

13. Today’s Objectives Students will perform a matched-pairs t procedure Students will use the TI to calculate one-sample confidence intervals Students will use the TI to calculate one-sample t-tests California Standard 20.0 Students are familiar with the t distributions and t test and understand their uses.

14. Homework Read pages 598 – 604 Do problems 12 - 14