A linguist is interested in current baby name trends in Fulton County. He is particularly interested in name length. To begin his study, he noted the number of letters in the first names of 450 randomly selected babies born in Fulton County last year. The linguist found a 90% confidence interval of (4.8,5.2) for the mean length of baby names in Fulton County last year.
Is the following conclusion valid?
There is a 10% chance that the mean length of baby names in Fulton County last year is not in the interval (4.8,5.2). no or yes

The given conclusion is **not valid**.

A confidence interval is interpreted in a specific way: a 90% confidence interval means that if we were to take many random samples and compute confidence intervals in the same way, 90% of those intervals would contain the true population mean. It does **not** mean there is a 10% chance that the true population mean is outside the given interval.

Once the confidence interval is computed, the true mean either is or is not in that interval. We don't assign probabilities to the population mean being inside or outside a particular interval once it's established. The 90% confidence refers to the method, not to the specific interval.

Would you like further explanation or details?

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Here are 5 related questions to expand your understanding:
1. How is a confidence interval calculated for a sample mean?
2. What factors affect the width of a confidence interval?
3. How would increasing the confidence level to 95% affect the interval?
4. What assumptions must be met for the confidence interval to be valid?
5. How is sample size related to the accuracy of the confidence interval?

**Tip:** Remember, confidence intervals refer to the reliability of the **method**, not the probability of where the true parameter lies once the interval is computed.

A linguist is interested in current baby name trends in Fulton County. He is particularly interested in name length. To begin his study, he noted the number of letters in the first names of 450 randomly selected babies born in Fulton County last year. The linguist found a 90% confidence interval of (4.8, 5.2) for the mean length of baby names in Fulton County last year. Is the following conclusion valid? There is a 10% chance that the mean length of baby names in Fulton County last year is not in the interval (4.8, 5.2).

Understand how to interpret a 90% confidence interval of (4.8, 5.2) for the mean length of baby names in Fulton County. This problem covers key statistical concepts such as confidence intervals, sampling, and the Central Limit Theorem. Suitable for high school statistics students in Grades 11-12.

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