Question 1186541
Here's how to calculate the confidence interval for the proportion of ASD in Arizona:

1. **Calculate the sample proportion (p̂):**

   p̂ = (Number of children with ASD) / (Total number of children)
   p̂ = 507 / 32601
   p̂ ≈ 0.01555

2. **Find the critical z-score:**

   *   For a 99% confidence level, alpha (α) is 1 - 0.99 = 0.01.
   *   Since confidence intervals are two-tailed, divide alpha by 2: 0.01 / 2 = 0.005.
   *   Find the z-score that corresponds to 0.005 in each tail (or 0.995 in the center).  Using a z-table or calculator, the z-score is approximately 2.576.

3. **Calculate the standard error (SE):**

   SE = sqrt[ (p̂ * (1 - p̂)) / n ]
   SE = sqrt[ (0.01555 * (1 - 0.01555)) / 32601 ]
   SE ≈ sqrt(0.00000472)
   SE ≈ 0.00217

4. **Calculate the margin of error (ME):**

   ME = z * SE
   ME = 2.576 * 0.00217
   ME ≈ 0.00559

5. **Calculate the confidence interval:**

   Lower Bound = p̂ - ME = 0.01555 - 0.00559 ≈ 0.00996
   Upper Bound = p̂ + ME = 0.01555 + 0.00559 ≈ 0.02114

6. **Express the confidence interval:**

   The 99% confidence interval for the proportion of ASD in Arizona is approximately (0.00996, 0.02114).

**Interpretation:**

We are 99% confident that the true proportion of children in Arizona with ASD in 2008 was between 0.996% and 2.114%.