Explanation:
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.