Question

State the conclusion of the test based on this p-value in terms of "Reject \(H_{0} "\) or "Do not reject \(H_{0} "\), if we use a \(5 \%\) significance level. p-value \(=0.0007\)

Short answer

Given that the p-value of 0.0007 is less than the significance level of 5% or 0.05, we reject the null hypothesis \(H_{0}\).

Step-by-step solution

Understand Terminologies

In hypothesis testing, the null hypothesis (\(H_{0}\)) represents a statement of no effect or no difference. The p-value is the probability, under the null hypothesis about the unknown distribution, of randomly drawing a value equal to or more extreme than the one obtained by testing. The significance level, often denoted by \(α\), is a threshold pre-determined at which if the calculated p-value in the test is less than this level, we reject the null hypothesis in favor of the alternative hypothesis.

Comparing the P-Value with the Significance Level

In this case, the given p-value is 0.0007, and the significance level is 5% or 0.05. We determine whether to reject the null hypothesis \(H_{0}\) based on whether the p-value is less than or equal to the significance level.

Formulate the Conclusion

Seeing that 0.0007 is less than 0.05, we would reject the null hypothesis \(H_{0}\). However, it is important to remember that rejecting the null hypothesis does not prove the alternative hypothesis; it merely provides evidence to suggest the alternative hypothesis may be true.