Hypothesis Test Process

Hypothesis Testing Process

1. State \(H_0\), \(H_a\), and pick \(\alpha\)
   
2. Calculate the Test Statistic (evidence against \(H_0\))
   
3. Calculate the P-Value (the probability of observing our test statistic or more extreme, if \(H_0\) were true)
   
4. Compare P-value to \(\alpha\)
   
5. Check the test requirements
   
6. Make a conclusion

Hypothesis Test Conclusions

1. \(\text{P-value} < \alpha\):
   • Reject the null hypothesis, \(H_0\), in favor of the alternative
     
   • “When \(P\) is low, reject \(H_0\)”
     
   • Sufficient Evidence to support the alternative
     1. Bring back to context of the research question. For example: I have sufficient evidence to suggest that Brother Cannon’s students are, on average, more agreeable than the general population.
        
   • Opportunity for a Type I Error, rejecting a true null hypothesis
2. \(\text{P-value} \ge \alpha\):
   • Fail to Reject the null hypothesis, \(H_0\)
     
   • Insufficient Evidence to support the alternative
     1. Bring back to context of the research question. For example: I have insufficient evidence to suggest that Brother Cannon’s students are, on average, less open than the general population.