Financial Risk Manager Part 1
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For a sample of the past 28 monthly stock returns for Bidco Inc., the mean return is 5% and the sample standard deviation is 15%. Assume that the population variance is unknown.
The related t-table values are given below, where (t_ij) denotes the (100 – j)th percentile of t-distribution value with i degrees of freedom):
t_{27,0.025} 2.05
t_{27,0.05} 1.70
t_{26,0.025} 2.06
t_{26,0.05} 1.71
t_{27,0.025} 2.05
t_{27,0.05} 1.70
t_{26,0.025} 2.06
t_{26,0.05} 1.71
What is the 95% confidence interval for the mean monthly return?
Other
Community
NNikitesh
A
[0.00181, 0.0989]
B
[-0.0084, 0.1084]
C
[-0.00811, 0.10811]
D
[0.02135, 0.07835]
Explanation:
Explanation:
To calculate the 95% confidence interval for the mean when the population variance is unknown, we use the t-distribution.
Step 1: Identify the parameters
- Sample mean (x̄) = 5% = 0.05
- Sample standard deviation (s) = 15% = 0.15
- Sample size (n) = 28
- Degrees of freedom (df) = n - 1 = 28 - 1 = 27
- Confidence level = 95%
Step 2: Determine the critical t-value For a 95% confidence interval with two tails, we need t_{27,0.025} = 2.05 (from the provided table)
Step 3: Calculate the standard error Standard error (SE) = s / √n = 0.15 / √28 ≈ 0.15 / 5.2915 ≈ 0.02835
Step 4: Calculate the margin of error Margin of error = t-value × SE = 2.05 × 0.02835 ≈ 0.05811
Step 5: Construct the confidence interval CI = x̄ ± margin of error = 0.05 ± 0.05811 = [-0.00811, 0.10811]
Why other options are incorrect:
- A [0.00181, 0.0989]: Uses incorrect critical value or calculation
- B [-0.0084, 0.1084]: Uses approximate calculation
- D [0.02135, 0.07835]: Uses z-value (1.96) instead of t-value, or incorrect standard error calculation
Key Concept: When population variance is unknown and sample size is relatively small (n < 30), we use the t-distribution rather than the normal distribution to construct confidence intervals.
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