Question

We have given the P-value for a hypothesis test. For each exercise determine the strength of the evidence against null hypothesis.

Given $P-value\mathrm{is}0.004.$

Short answer

The P-value is 0.004, which is lower than the 0.01 threshold.

The null hypothesis is obviously strongly rejected as a result of the conditions.

Step-by-step solution

Step 1. Given

The given$P-valueis0.004.$

Step 2. Conditions for evaluating strength of the evidence 

Criteria for testing the strength of evidence from P values:

$-0.10<P-value,$weak or no evidence to contradict the null hypothesis.

$-0.05<P-value\le 0.10,$moderate evidence contradict the null hypothesis.

$-0.01<P-value<0.05,$strong evidence contradict the null hypothesis.

$-P-value<0.01,$the strongest evidence contradict the null hypothesis.

Conclusion

The P-value is 0.004, which is lower than the 0.01 threshold.

That is, $P-value(=0.004)<0.01.$

The null hypothesis is obviously strongly rejected as a result of the conditions.