Question 1181343
Here's how to construct and interpret the confidence interval:

**a) Constructing a 95% Confidence Interval:**

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

p̂ = (Number of students who believe TV is a luxury) / (Total number of students)
p̂ = 521 / 1003
p̂ ≈ 0.52

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

For a 95% confidence level, the alpha (α) level is 1 - 0.95 = 0.05.  We need to find the z-score that corresponds to an area of 0.975 (1 - α/2) in the standard normal distribution.  This z-value is approximately 1.96. You can find this using a z-table or calculator.

3. **Calculate the margin of error (E):**

E = z * √(p̂(1 - p̂) / n)
E = 1.96 * √(0.52 * (1 - 0.52) / 1003)
E ≈ 1.96 * √(0.2496 / 1003)
E ≈ 1.96 * 0.0157
E ≈ 0.0308

4. **Construct the confidence interval:**

Lower Bound = p̂ - E = 0.52 - 0.0308 ≈ 0.4892
Upper Bound = p̂ + E = 0.52 + 0.0308 ≈ 0.5508

Therefore, the 95% confidence interval is approximately (0.4892, 0.5508).

**b) Interpretation of the Confidence Interval:**

We are 95% confident that the true population proportion of community college students who believe television is a luxury they can live without is between 48.92% and 55.08%.  This means that if we were to repeat this study many times and calculate a 95% confidence interval each time, 95% of those intervals would contain the true population proportion.  It's important to remember that this interval is an estimate, and the true proportion may or may not fall within this range.