To determine if the statement is TRUE or FALSE, we need to assess whether the interval 2.07 to 2.33 represents an approximate 95% confidence interval for household size, based on the given sample data.

Step 1: Understand the information provided

• Sample size (n) = 900 households
• Sample mean (𝑥̄) = 2.2 people
• Sample standard deviation (s) = 2 people

Step 2: Use the Empirical Rule (68-95-99.7 Rule)

For a normal distribution:

• About 68% of values lie within ±1 standard deviation from the mean.
• About 95% of values lie within ±2 standard deviations from the mean.

Here, the standard deviation is 2 people, and the sample mean is 2.2 people.

Step 3: Calculate the range for 95% of values

To find the range where approximately 95% of household sizes fall:

• Subtract 2 times the standard deviation from the mean:
  $2.2 - 2 \times 2 = 2.2 - 4 = -1.8$
• Add 2 times the standard deviation to the mean:
  $2.2 + 2 \times 2 = 2.2 + 4 = 6.2$

Thus, approximately 95% of the households should have sizes between -1.8 and 6.2 people. Clearly, this range (from -1.8 to 6.2) does not match the stated range of 2.07 to 2.33 people.

Step 4: Conclusion

The interval 2.07 to 2.33 is much narrower than the 95% range (which should be from -1.8 to 6.2), so the statement is FALSE.

Final Answer: FALSE

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Would you like further details or have any questions? Here are some related questions to explore:

1. How do you compute confidence intervals for a sample mean?
2. What is the difference between sample standard deviation and population standard deviation?
3. How does the central limit theorem affect the interpretation of sample data?
4. What is the significance of a normal distribution in real-world data analysis?
5. How would you adjust for outliers when calculating averages in a sample?

Tip: Always check the assumptions behind the use of the empirical rule, such as normality of the data or large enough sample size.