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Answer: The critical value of the test is 1.65; the manager should reject the null hypothesis and conclude that the mean return is significantly greater than zero.
## Explanation This is a **one-tailed hypothesis test** for the mean weekly return being greater than zero. ### Hypothesis Setup: - **Null Hypothesis (H₀):** mean return = 0 - **Alternative Hypothesis (H₁):** mean return > 0 ### Key Parameters: - **Test statistic:** 2.84 - **Significance level:** 5% (α = 0.05) - **Sample size:** Weekly data over 1 year (approximately 52 observations) ### Critical Value Determination: For a **one-tailed test** at 5% significance level: - The critical z-value is **1.65** - This represents the 95th percentile of the standard normal distribution ### Decision Rule: - **Reject H₀** if test statistic > critical value - **Do not reject H₀** if test statistic ≤ critical value ### Analysis: - Test statistic (2.84) > Critical value (1.65) - Therefore, we **reject the null hypothesis** ### Conclusion: The manager should conclude that the mean weekly return is **statistically significantly greater than zero** at the 5% significance level. ### Why Other Options Are Incorrect: - **A & C:** Use 1.96 as critical value, which is for a **two-tailed test** at 5% significance level - **D:** Uses correct critical value (1.65) but makes wrong decision - fails to reject null when test statistic clearly exceeds critical value This test demonstrates that the currency swap portfolio is generating statistically significant positive returns.
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A trading desk manager at a financial institution oversees the maintenance of currency swap lines and has gathered weekly returns data for a portfolio of currency swaps over the last year. The manager calculates the mean weekly portfolio return as 0.71%, and the sample standard deviation of returns as 0.52%. To determine the statistical significance of the mean weekly return being greater than zero, the manager decides to conduct a hypothesis test at a 5% level of significance. If the manager calculates the test statistic as 2.84, which of the following is correct?
A
The critical value of the test is 1.96; the manager should reject the null hypothesis and conclude that the mean return is significantly greater than zero.
B
The critical value of the test is 1.65; the manager should reject the null hypothesis and conclude that the mean return is significantly greater than zero.
C
The critical value of the test is 1.96; the manager should not reject the null hypothesis and therefore cannot conclude that the mean return is not significantly greater than zero.
D
The critical value of the test is 1.65; the manager should not reject the null hypothesis and therefore cannot conclude that the mean return is not significantly greater than zero.