Apply the components of hypothesis testing to the following scenario:

You come home late Tuesday night from a work meeting and your teenager is still up when they should be in bed. You ask if they are ready for bed and they reply yes, yet you believe they are not telling the truth. You suspect they have not done their homework (completed 15 Algebra problems) or finished their chores (feed the dog) or gotten ready for bed (brushed their teeth).

1. Hypothesize your suspicion, keeping in mind, we do not assume someone is guilty, we need to prove guilt. Write out in words your null and alternative hypotheses.

2. Think about the "data" for proving guilt for this scenario. List the "data" you would be looking for as indicators of guilt.

3. We use a p-value to indicate if we are rejecting or not rejecting the null hypothesis. Suppose we could calculate a p-value for this scenario it is p=0.02. What does this mean? Explain if you would reject or not reject the null hypothesis based on this p-value.

4. Discuss the difference between a Type I error and a Type II error in terms of this scenario.

5. What are the implications of a Type I error in terms of this scenario?

6. What are the implications of a Type II error in terms of this scenario?