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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.
ExplanationB is correct. Note that the null hypothesis and alternative hypothesis for this one-tailed test are constructed as follows: Ho: mean return = 0 Hi: mean return > 0 When testing against a one-sided (upper) alternative, the decision rejects the null if the test statistic is greater than the critical value. Since the test statistic of 9.85 > 1.65 which is the critical value of a one-tailed test for a 5% level of significance (the critical z values for a 95% confidence interval are either -1.65 or +1.65 if only one tail is considered), we reject the null hypothesis and conclude that the sample return value is statistically different from the hypothesized value of 0. D is incorrect. See explanation given in B above. A and C are incorrect. They present a critical value that is based on a either a two-sided 5% level of significance or a one-sided 2.5% level of significance.
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A trading desk manager at a financial institution oversees currency swap lines and has gathered weekly return data over a year for a portfolio of currency swaps. The mean weekly return calculated from this data is 0.71%, with a sample standard deviation of 0.52%. To determine if the mean weekly return is significantly greater than zero, a hypothesis test is conducted at a 5% significance level. With the test statistic calculated as 2.84, which of the following conclusions 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.