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Answer: [0.02054, 0.03646]
**Explanation:** To calculate the 95% confidence interval for the mean return: 1. **Given parameters:** - Sample mean (x̄) = 2.85% = 0.0285 - Sample standard deviation (s) = 1.6% = 0.016 - Sample size (n) = 18 - Confidence level = 95% 2. **Degrees of freedom:** - df = n - 1 = 18 - 1 = 17 3. **Critical t-value:** - For a 95% confidence interval, we need a two-tailed test with α = 0.05 - Each tail has α/2 = 0.025 - From the t-table, with df = 17 and α = 0.025 (one-tailed), t₁₇,₀.₀₂₅ = 2.11 4. **Standard error:** - Standard error = s/√n = 0.016/√18 = 0.016/4.2426 = 0.003771 5. **Margin of error:** - Margin = t × standard error = 2.11 × 0.003771 = 0.00796 6. **Confidence interval:** - Lower bound = 0.0285 - 0.00796 = 0.02054 - Upper bound = 0.0285 + 0.00796 = 0.03646 - CI = [0.02054, 0.03646] **Key points:** - We use t-distribution because population variance is unknown - Confidence intervals are two-sided, so we use α/2 = 0.025 - Degrees of freedom = n - 1 = 17 - The calculation matches option D exactly
Author: Nikitesh Somanthe
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Using returns observed over the past 18 monthly, an analyst has estimated the mean monthly return of stock A to be 2.85% with a standard deviation of 1.6%. One-tailed t-distribution table
| Degrees of freedom | α = 0.1 | α = 0.05 | α = 0.025 |
|---|---|---|---|
| 14 | 1.35 | 1.76 | 2.15 |
| 15 | 1.34 | 1.75 | 2.13 |
| 16 | 1.34 | 1.75 | 2.12 |
| 17 | 1.33 | 1.74 | 2.11 |
| 18 | 1.33 | 1.73 | 2.10 |
Using the t-table above, the 95% confidence interval for the mean return is between:
A
[0.02031, 0.03688]
B
[0.02051, 0.03650]
C
[0.02194, 0.03506]
D
[0.02054, 0.03646]
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