Question 1182178
Here's how to calculate the confidence interval for the population standard deviation (σ):

1. **Identify the given information:**

*   Confidence level = 95%
*   Sample size (n) = 51
*   Sample mean (x̄) = $60,100 (This is not needed for the standard deviation confidence interval)
*   Sample standard deviation (s) = $19,008

2. **Determine the degrees of freedom:**

Degrees of freedom (df) = n - 1 = 51 - 1 = 50

3. **Find the critical chi-square values:**

For a 95% confidence level, α = 1 - 0.95 = 0.05.  We need to find the chi-square values for α/2 and 1-α/2.

*   α/2 = 0.05 / 2 = 0.025
*   1 - α/2 = 1 - 0.025 = 0.975

Using a chi-square distribution table or calculator, look up the values for df = 50:

*   χ²(0.025, 50) ≈ 71.42
*   χ²(0.975, 50) ≈ 32.36

4. **Calculate the confidence interval:**

The formula for the confidence interval for σ is:

√[((n-1)s²) / χ²(α/2, df)] < σ < √[((n-1)s²) / χ²(1-α/2, df)]

Substitute the values:

√[((50) * (19008)²) / 71.42] < σ < √[((50) * (19008)²) / 32.36]

√[361304448.3 / 71.42] < σ < √[361304448.3 / 32.36]

√5059639.46 < σ < √11162002.11

$2249.36 < σ < $3340.96 (approximately)

Therefore, the 95% confidence interval for the population standard deviation (σ) is approximately **$16,942 < σ < $22,500**.