Financial Risk Manager Part 1
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The mean return of a sample of 36 BB+ corporate bonds is 7.5%, and the sample's standard deviation is 14%. Assuming that the population is normally distributed and the population variance is unknown, what is the 95% confidence interval for the population mean?
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Community
NNikitesh
A
[2.77%; 12.23%]
B
[2.93%; 12.06%]
C
[3.56%; 11.43%]
D
[4.12%; 13.3%]
Explanation:
Since the population variance is unknown and the population is normally distributed, we use a t-statistic. The t-statistic for a 95% confidence interval and 35 degrees of freedom (df=n-1) is 2.030.
The standard error of the sample = Standard Deviation of sample mean / √Sample size = 14/√36 = 14/6 = 2.333
The confidence interval is calculated as: Lower bound = 7.5 - (2.030 * 2.333) = 7.5 - 4.73 = 2.77% Upper bound = 7.5 + (2.030 * 2.333) = 7.5 + 4.73 = 12.23%
Therefore, the 95% confidence interval is [2.77%; 12.23%].
Using a t-distribution reliability factor is appropriate when the population variance is unknown, even with relatively large samples. The t-distribution provides more conservative (wider) confidence intervals compared to the normal distribution in such cases.
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