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 D) = 36.19

Question

Quizplus · Accepted Answer

We can use the formula for the test statistic of a one-sample t-test:

t = (x̄ - μ) / (s / sqrt(n))

where x̄ is the sample mean, μ is the hypothesized population mean, s is the sample standard deviation, and n is the sample size.

In this case, the null hypothesis is that the variance is not more than 280%. So we can calculate the hypothesized standard deviation as sqrt(280%) = 16.73%.

Plugging in the values, we get:

t = (12.1% - 0%) / (36.1% / sqrt(20)) = 2.58

Comparing this to the t-distribution with 19 degrees of freedom (since df = n - 1 = 20 - 1 = 19), we find a p-value of approximately 0.018.

Since this is less than the typical significance level of 0.05, we reject the null hypothesis and conclude that there is sufficient evidence to suggest that the variance is indeed more than 280%.

Looking at the answer choices, we see that only option B matches our calculated t-value of 2.58. Therefore, the correct answer is B.

A Financial Analyst Maintains That the Risk, Measured by the Variance