The superintendent of Morristown School District is concerned about the study habits of students in the district. He had guidance counselors throughout the city ask 75 randomly chosen students how many hours they study each day. The superintendent computed a 90% confidence interval (2.9,3.1) for the mean number of hours students in Morristown study each day.
Is the following conclusion valid?
If the counselors take another random sample, there is a 10% chance that the mean number of hours students in Morristown study each day will not be in the new sample's 90% confidence interval. no or yes

The conclusion is valid: **yes**.

The reasoning behind this is that a confidence interval of 90% means that, if we were to take many different random samples of the same size (in this case, 75 students) and compute the confidence interval for each sample, approximately 90% of those intervals would contain the true population mean. 

This also means that 10% of the time, the confidence interval would not contain the true population mean. Therefore, if the counselors take another random sample, there is a 10% chance that the new confidence interval **does not** include the true population mean. This aligns with the meaning of the 90% confidence interval.

Would you like more details or further clarification?

Here are 5 related questions:
1. What happens if we increase the confidence level to 95%?
2. How is the confidence interval calculated for a population mean?
3. What assumptions are necessary for the confidence interval to be valid?
4. How does the sample size affect the width of the confidence interval?
5. What is the meaning of the true population mean in the context of confidence intervals?

**Tip:** Increasing the confidence level will make the confidence interval wider, as it requires more certainty that the interval captures the true population mean.

The superintendent of Morristown School District is concerned about the study habits of students in the district. He had guidance counselors throughout the city ask 75 randomly chosen students how many hours they study each day. The superintendent computed a 90% confidence interval (2.9, 3.1) for the mean number of hours students in Morristown study each day. Is the following conclusion valid? If the counselors take another random sample, there is a 10% chance that the mean number of hours students in Morristown study each day will not be in the new sample's 90% confidence interval. no or yes

Explore how to interpret a 90% confidence interval for the mean number of study hours in Morristown School District. This problem focuses on confidence intervals, sampling, and statistical reasoning, with a clear explanation of why there's a 10% chance the interval doesn't contain the true population mean. Suitable for Grades 10-12.

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