A financial analyst maintains that the risk,measured by the variance,of investing in emerging markets is more than 280(%)².Data on 20 stocks from emerging markets revealed the following sample results: = 12.1% and s² = 361(%)².Assume that the returns are normally distributed.Which of the following is the correct value of the test statistic? A) = 36.19 B) = 24.50 C) = 24.50

Question

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We want to test if the variance (σ^2) of the population is greater than 280.

Null Hypothesis: σ^2 ≤ 280
Alternative Hypothesis: σ^2 > 280

Sample size (n) = 20
Sample variance (s^2) = (361/100)^2 = 1.3021
Significance level (α) = 0.05 (assuming a two-tailed test)

We will use the chi-square test with n-1 degrees of freedom, where n is the sample size.

Test Statistic: 
χ^2 = (n-1) * s^2 / σ^2 = 19 * 1.3021 / 280 = 0.8853

The critical value at α = 0.05 and 19 degrees of freedom is 30.14 (from chi-square table). Since the test statistic (0.8853) is less than the critical value (30.14), we fail to reject the null hypothesis.

Conclusion: There is not enough evidence to support the claim that the variance of investing in emerging markets is more than 280.

Out of the given choices, option B has a test statistic of 24.50, which is the correct value of the chi-square test statistic.

A Financial Analyst Maintains That the Risk,measured by the Variance,of