Let's analyze this hypothesis testing problem step-by-step.

1. Null Hypothesis $H_0$: The null hypothesis is that your friend's average exam score is at least 98%. This is mathematically represented as: $H_0: \mu \geq 0.98$ This aligns with the claim made by your friend.

2. Alternative Hypothesis $H_a$: The alternative hypothesis is that your friend's average exam score is less than 98%, represented as: $H_a: \mu < 0.98$ This is what we would conclude if there’s evidence that the average is actually below 98%.

3. Significance Level and p-value: The significance level (alpha) is 5% (0.05), which is the threshold for determining statistical significance. The p-value obtained from the test is 0.07.

4. Conclusion:

   • Since the p-value (0.07) is greater than the significance level (0.05), we do not reject the null hypothesis.
   • Therefore, the correct conclusion is:
     • "You cannot conclude that your friend doesn’t average a 98% on his exams."

Would you like further details on any part of this explanation?

Here are some related questions for further exploration:

1. What would the conclusion be if the p-value were 0.03 instead?
2. How does changing the significance level to 1% (0.01) affect the conclusion?
3. What are Type I and Type II errors in the context of this hypothesis test?
4. How would you set up a hypothesis test if the claim was that the average score was exactly 98%?
5. What are the possible steps if we wanted to increase the sample size to reduce uncertainty?

Tip: In hypothesis testing, if the p-value is less than the significance level, we reject the null hypothesis. If it’s greater, we fail to reject the null hypothesis.