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Answer: Can conclude that the standard deviation of returns is higher than 14%.
## Explanation This is a chi-square test for variance. The test statistic is calculated as: \[ \chi^2 = \frac{(n-1)s^2}{\sigma_0^2} \] Where: - n = 61 (sample size) - s = 21% (sample standard deviation) - σ₀ = 14% (hypothesized standard deviation) - df = n - 1 = 60 \[ \chi^2 = \frac{(61-1) \times (0.21)^2}{(0.14)^2} = \frac{60 \times 0.0441}{0.0196} = \frac{2.646}{0.0196} = 135 \] The critical value at α = 0.05 with df = 60 is 79.08. Since our test statistic (135) is greater than the critical value (79.08), we reject the null hypothesis that the population standard deviation is 14% or less. Therefore, we can conclude that the standard deviation of returns is higher than 14%.
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Using a sample size of 61 observations, an analyst determines that the standard deviation of the returns from a stock is 21%. Using a 0.05 significance level, the analyst: (If df = 60 and p = 0.05, the critical value is 79.08)
A
Can conclude that the standard deviation of returns is higher than 14%.
B
Cannot conclude that the standard deviation of returns is higher than 14%.
C
Can conclude that the standard deviation of returns is not higher than 14%.
D
None of the above.
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