NO.PZ2023091601000062
问题如下：
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?
选项：
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.
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.
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.
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.
解释：
B is correct. Note
that the null hypothesis and alternative hypothesis for this one-tailed test
are constructed as follows: H0: mean return = 0 H1: 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.
- 怎么判断这是一个one tailed 的test
- 答案中提到critical value是9.85，请问是怎么得出来的？
