1. Statistics: Unlocking the Power of Data Lock 5 Section 4.3 Determining Statistical Significance

2. Statistics: Unlocking the Power of Data Lock 5 Review The smaller the p-value the a) stronger the evidence against the null hypothesis b) stronger the evidence for the null hypothesis If the p-value is low, then it would be very rare to get results as extreme as those observed, if the null hypothesis were true. This suggests that the null hypothesis is probably not true!

3. Statistics: Unlocking the Power of Data Lock 5 Resveratrol, an ingredient in red wine and grapes, has been shown to promote weight loss in rodents, and has recently been investigated in primates (specifically, the Grey Mouse Lemur). A sample of lemurs had various measurements taken before and after receiving resveratrol supplementation for 4 weeks Red Wine and Weight Loss BioMed Central (2010, June 22). “Lemurs lose weight with ‘life-extending’ supplement resveratrol. Science Daily.

4. Statistics: Unlocking the Power of Data Lock 5 Red Wine and Weight Loss In the test to see if the mean resting metabolic rate is higher after treatment, the p-value is 0.013. Using  = 0.05, is this difference statistically significant? (should we reject H 0 ?) a) Yes b) No The p-value is lower than  = 0.05, so the results are statistically significant and we reject H 0.

5. Statistics: Unlocking the Power of Data Lock 5 Red Wine and Weight Loss In the test to see if the mean body mass is lower after treatment, the p-value is 0.007. Using  = 0.05, is this difference statistically significant? (should we reject H 0 ?) a) Yes b) No The p-value is lower than  = 0.05, so the results are statistically significant and we reject H 0.

6. Statistics: Unlocking the Power of Data Lock 5 Red Wine and Weight Loss In the test to see if locomotor activity changes after treatment, the p-value is 0.980. Using  = 0.05, is this difference statistically significant? (should we reject H 0 ?) a) Yes b) No The p-value is not lower than  = 0.05, so the results are not statistically significant and we do not reject H 0.

7. Statistics: Unlocking the Power of Data Lock 5 Red Wine and Weight Loss In the test to see if mean food intake changes after treatment, the p-value is 0.035. Using  = 0.05, is this difference statistically significant? (should we reject H 0 ?) a) Yes b) No The p-value is lower than  = 0.05, so the results are statistically significant and we reject H 0.

8. Statistics: Unlocking the Power of Data Lock 5 Statistical Conclusions In a hypothesis test of H 0 :  = 10 vs H a :  < 10 the p-value is 0.002. With α = 0.05, we conclude: a) Reject H 0 b) Do not reject H 0 c) Reject H a d) Do not reject H a The p-value of 0.002 is less than α = 0.05, so we reject H 0

9. Statistics: Unlocking the Power of Data Lock 5 Statistical Conclusions In a hypothesis test of H 0 :  = 10 vs H a :  < 10 the p-value is 0.002. With α = 0.01, we conclude: a) There is evidence that  = 10 b) There is evidence that  < 10 c) We have insufficient evidence to conclude anything

10. Statistics: Unlocking the Power of Data Lock 5 Statistical Conclusions In a hypothesis test of H 0 :  = 10 vs H a :  < 10 the p-value is 0.21. With α = 0.01, we conclude: a) Reject H 0 b) Do not reject H 0 c) Reject H a d) Do not reject H a The p-value of 0.21 is not less than α = 0.01, so we do not reject H 0

11. Statistics: Unlocking the Power of Data Lock 5 Statistical Conclusions In a hypothesis test of H 0 :  = 10 vs H a :  < 10 the p-value is 0.21. With α = 0.01, we conclude: a) There is evidence that  = 10 b) There is evidence that  < 10 c) We have insufficient evidence to conclude anything

12. Statistics: Unlocking the Power of Data Lock 5 How many of the following p-values are significant at the 5% level? 0.005 0.03 0.08 0.42 0.79 A. 1 B. 2 C. 3 D. 4 E. 0 or 5 Two of the p-values are less than 0.05 so are significant at a 5% level.

13. Statistics: Unlocking the Power of Data Lock 5 How many of the following p-values are significant at the 10% level? 0.005 0.03 0.08 0.42 0.79 A. 1 B. 2 C. 3 D. 4 E. 0 or 5 Three of the p-values are less than 0.10 so are significant at a 10% level.

14. Statistics: Unlocking the Power of Data Lock 5 How many of the following p-values are significant at the 1% level? 0.005 0.03 0.08 0.42 0.79 A. 1 B. 2 C. 3 D. 4 E. 0 or 5 Only one of the p-values is less than 0.01 so only one is significant at a 1% level.

15. Statistics: Unlocking the Power of Data Lock 5 A new blood thinning drug is being tested against the current drug in a double-blind experiment. Is there evidence that the mean blood thinness rating is higher for the new drug? Using n for the new drug and o for the old drug, which of the following are the null and alternative hypotheses? A. H 0 :  n >  o vs H a :  n =  o B. H 0 :  n =  o vs H a :  n   o C. H 0 :  n =  o vs H a :  n >  o D.H 0 : vs H a : E.H 0 : vs H a :

16. Statistics: Unlocking the Power of Data Lock 5 A new blood thinning drug is being tested against the current drug in a double-blind experiment, and the hypotheses are: H 0 :  n =  o vs H a :  n >  o What does a Type 1 Error mean in this situation? A.We reject H 0 B. We do not reject H 0 C.We find evidence the new drug is better when it is really not better. D.We are not able to conclude that the new drug is better even though it really is. E.We are able to conclude that the new drug is better.

17. Statistics: Unlocking the Power of Data Lock 5 A new blood thinning drug is being tested against the current drug in a double-blind experiment, and the hypotheses are: H 0 :  n =  o vs H a :  n >  o What does a Type 2 Error mean in this situation? A.We reject H 0 B. We do not reject H 0 C.We find evidence the new drug is better when it is really not better. D.We are not able to conclude that the new drug is better even though it really is. E.We are able to conclude that the new drug is better.

18. Statistics: Unlocking the Power of Data Lock 5 A new blood thinning drug is being tested against the current drug in a double-blind experiment, and the hypotheses are: H 0 :  n =  o vs H a :  n >  o If the new drug has potentially serious side effects, we should pick a significance level that is: A.Relatively small (such as 1%) B.Middle of the road (5%) C.Relatively large (such as 10%) Since a Type 1 error would be serious, we use a small significance level.

19. Statistics: Unlocking the Power of Data Lock 5 A new blood thinning drug is being tested against the current drug in a double-blind experiment, and the hypotheses are: H 0 :  n =  o vs H a :  n >  o If the new drug has no real side effects and costs less than the old drug, we might pick a significance level that is: A.Relatively small (such as 1%) B.Middle of the road (5%) C.Relatively large (such as 10%) Since a Type 1 error is not at all serious here, we might use a large significance level.