Interpreting the Weight of Evidence against the Null Hypothesis
If the p-value for testing H0 is less than
• .10, we have some evidence that H0 is false.
• .05, we have strong evidence that H0 is false.
• .01, we have very strong evidence that H0 is false.
• .001, we have extremely strong evidence that H0 is false.
We will frequently use these conclusions in future examples. Understand, however, that there are really no sharp borders between different weights of evidence. Rather, there is really only increasingly strong evidence against the null hypothesis as the p-value decreases.
For example, recall that the p-value for testing H0: μ = 50 versus Ha: μ > 50 in the trash bag case is .0139. This p-value is less than .05 but not less than .01. Therefore, we have strong evidence, but not very strong evidence, that H0: μ = 50 is false and Ha: μ > 50 is true. That is, we have strong evidence that the mean breaking strength of the new trash bag exceeds 50 pounds. As another example, the p-value for testing H0: μ = 19.5 versus Ha: μ < 19.5 in the payment time case is .0038. This p-value is less than .01 but not less than .001. Therefore, we have very strong evidence, but not extremely strong evidence, that H0: μ = 19.5 is false and Ha: μ < 19.5 is true. That is, we have very strong evidence that the new billing system has reduced the mean payment time by more than 50 percent. Finally, the p-value for testing H0: μ = 330 versus Ha: μ ≠ 330 in the Valentine’s Day chocolate case is .3174. This p-value is greater than .10. Therefore, we have little evidence that H0: μ = 330 is false and Ha: μ ≠ 330 is true. That is, we have little evidence that the increase in the mean order quantity of the valentine box by large retail stores will differ from ten percent.