Determining Statistical Significance Section 4.3 Determining Statistical Significance

Using the randomization distribution below to test H0 :  = 0 vs Ha :  > 0 Which sample statistic shows the most evidence for the alternative hypothesis? A. r = 0.1 B. r = 0.3 C. r = 0.5 r = 0.5 shows the most evidence and p = 0.005 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.

Using the randomization distribution below to test H0 :  = 0 vs Ha :  > 0 Therefore, which p-value shows the most evidence for the alternative hypothesis? A. 0.35 B. 0.15 C. 0.005 r = 0.5 shows the most evidence and p = 0.005 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.

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!

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.

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.

p-value and H0 Two different studies obtain two different p-values. Study A obtained a p-value of 0.002 and Study B obtained a p-value of 0.2. 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.

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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 H0?) Yes No The p-value is lower than  = 0.05, so the results are statistically significant and we reject H0.

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 H0?) Yes No The p-value is lower than  = 0.05, so the results are statistically significant and we reject H0.

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 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.

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 H0?) Yes No The p-value is lower than  = 0.05, so the results are statistically significant and we reject H0.

Statistical Conclusions In a hypothesis test of H0:  = 10 vs Ha:  < 10 the p-value is 0.002. With α = 0.05, we conclude: Reject H0 Do not reject H0 Reject Ha Do not reject Ha The p-value of 0.002 is less than α = 0.05, so we reject H0

Statistical Conclusions In a hypothesis test of H0:  = 10 vs Ha:  < 10 the p-value is 0.002. With α = 0.01, we conclude: There is evidence that  = 10 There is evidence that  < 10 We have insufficient evidence to conclude anything

Statistical Conclusions In a hypothesis test of H0:  = 10 vs Ha:  < 10 the p-value is 0.21. 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

Statistical Conclusions In a hypothesis test of H0:  = 10 vs Ha:  < 10 the p-value is 0.21. With α = 0.01, we conclude: There is evidence that  = 10 There is evidence that  < 10 We have insufficient evidence to conclude anything

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.

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.

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.