(d) Based on the the confidence interval constructed in part (a), is it likely that the mean mathematics SAT score for the entering freshman class is greater than 472?

It (is or is not) likely that the mean mathematics SAT score for the entering freshman class is greater than .

To determine if it is likely that the mean mathematics SAT score for the entering freshman class is greater than 472, we need to examine the confidence interval constructed in part (a).

The 80% confidence interval we constructed was:
\[ 426 < \mu < 456 \]

This interval provides a range within which we are 80% confident the true population mean (\(\mu\)) lies.

Since 472 is not within the range of 426 to 456, it suggests that it is unlikely for the true mean mathematics SAT score to be greater than 472.

Thus, it **is not** likely that the mean mathematics SAT score for the entering freshman class is greater than 472.

Would you like more details or have any questions?

Here are 5 questions you can ask:
1. How can we interpret a confidence interval in the context of hypothesis testing?
2. What are the implications of changing the confidence level on the width of the confidence interval?
3. Can you explain the difference between confidence intervals and prediction intervals?
4. How would we calculate a 90% confidence interval for the same data?
5. What assumptions are necessary for constructing a valid confidence interval?

**Tip:** Always check if the value you're interested in falls within the confidence interval. If it doesn't, it's unlikely that the population parameter matches that value, given the level of confidence specified.

Explore whether the mean mathematics SAT score for the entering freshman class is likely to be greater than 472. Understand the construction and interpretation of confidence intervals in hypothesis testing.

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