1. Determining Statistical Significance
Section 4.3
Determining Statistical Significance

2. Using the randomization distribution below to test
H0 :  = vs Ha :  > 0
Which sample statistic shows the most evidence for the alternative hypothesis?
A. r = B. r = C. r = 0.5
r = 0.5 shows the most evidence and p = shows the most evidence. Idea to get across: Sample statistics far out in the tail show the most evidence against the null, so small p-values show the most evidence.

3. Using the randomization distribution below to test
H0 :  = vs Ha :  > 0
Therefore, which p-value shows the most evidence for the alternative hypothesis?
A B C
r = 0.5 shows the most evidence and p = shows the most evidence. Idea to get across: Sample statistics far out in the tail show the most evidence against the null, so small p-values show the most evidence.

4. Small p-value The smaller the p-value the
stronger the evidence against the null hypothesis
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!

5. p-value and H0
Which of the following p-values gives the strongest evidence against H0?
0.005
0.1
0.32
0.56
0.94
The lower the p-value, the stronger the evidence against the null hypothesis.

6. p-value and H0
Which of the following p-values gives the strongest evidence against H0?
0.22
0.45
0.03
0.8
0.71
The lower the p-value, the stronger the evidence against the null hypothesis.

7. p-value and H0
Two different studies obtain two different p-values. Study A obtained a p-value of and Study B obtained a p-value of Which study obtained stronger evidence against the null hypothesis?
Study A
Study B
The lower the p-value, the stronger the evidence against the null hypothesis.

8. Red Wine and Weight Loss
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
BioMed Central (2010, June 22). “Lemurs lose weight with ‘life-extending’ supplement resveratrol. Science Daily.

9. Red Wine and Weight Loss
In the test to see if the mean resting metabolic rate is higher after treatment, the p-value is Using  = 0.05, is this difference statistically significant? (should we reject H0?)
Yes No
The p-value is lower than  = 0.05, so the results are statistically significant and we reject H0.

10. Red Wine and Weight Loss
In the test to see if the mean body mass is lower after treatment, the p-value is Using  = 0.05, is this difference statistically significant? (should we reject H0?)
Yes No
The p-value is lower than  = 0.05, so the results are statistically significant and we reject H0.

11. Red Wine and Weight Loss
In the test to see if locomotor activity changes after treatment, the p-value is Using  = 0.05, is this difference statistically significant? (should we reject H0?)
Yes No
The p-value is not lower than  = 0.05, so the results are not statistically significant and we do not reject H0.

12. Red Wine and Weight Loss
In the test to see if mean food intake changes after treatment, the p-value is Using  = 0.05, is this difference statistically significant? (should we reject H0?)
Yes No
The p-value is lower than  = 0.05, so the results are statistically significant and we reject H0.

13. Statistical Conclusions
In a hypothesis test of H0:  = 10 vs Ha:  < 10 the p-value is With α = 0.05, we conclude:
Reject H0
Do not reject H0
Reject Ha
Do not reject Ha
The p-value of is less than α = 0.05, so we reject H0

14. Statistical Conclusions
In a hypothesis test of H0:  = 10 vs Ha:  < 10 the p-value is With α = 0.01, we conclude:
There is evidence that  = 10
There is evidence that  < 10
We have insufficient evidence to conclude anything

15. Statistical Conclusions
In a hypothesis test of H0:  = 10 vs Ha:  < 10 the p-value is With α = 0.01, we conclude:
Reject H0
Do not reject H0
Reject Ha
Do not reject Ha
The p-value of 0.21 is not less than α = 0.01, so we do not reject H0

16. Statistical Conclusions
In a hypothesis test of H0:  = 10 vs Ha:  < 10 the p-value is With α = 0.01, we conclude:
There is evidence that  = 10
There is evidence that  < 10
We have insufficient evidence to conclude anything

17. How many of the following p-values are significant at the 5% level?
A B C D E. 0 or 5
Two of the p-values are less than 0.05 so are significant at a 5% level.

18. How many of the following p-values are significant at the 10% level?
A B C D E. 0 or 5
Three of the p-values are less than 0.10 so are significant at a 10% level.

19. How many of the following p-values are significant at the 1% level?
A B C D E. 0 or 5
Only one of the p-values is less than 0.01 so only one is significant at a 1% level.