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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?

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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.

Your friend claims that he averages a 98% on his exams. You want to test this claim. Identify the null and alternative hypotheses. Conduct a hypothesis test at the 5% significance level with a p-value of 0.07, and draw a conclusion.

Explore hypothesis testing with a problem where a student's average score claim is tested. Learn how to set up the null and alternative hypotheses, analyze the p-value at a 5% significance level, and interpret the results.

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