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.
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.
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.
老师好，依据题目背择假设是Ha大于0，没有问题，但是原假设为什么不是小于等于0？
