NO.PZ2023091601000053
问题如下：
Bob tests the null hypothesis
that the population mean is less than or equal to 45. From a population size of
3,000,000 people, 81 observations are randomly sampled. The corresponding
sample mean is 46.3 and sample standard deviation is 4.5. What is the value of
the appropriate test statistic for the test of the population mean, and what is
the correct decision at the 1 percent significance level?
选项：
A.
z = 0.29, and fail
to reject the null hypothesis.
B.
z = 2.60, and
reject the null hypothesis.
C.
t =
0.29, and accept the null hypothesis
D.
t = 2.60, and
neither reject nor fail to reject the null hypothesis.
解释：
A is incorrect. The
denominator of the z-test statistic is standard error instead of standard deviation.
If the denominator takes the value of standard deviation 4.5, instead of
standard error 4.5/sqrt(81), the z-test statistic computed will be z = 0.29,
which is incorrect.
B is correct. The
population variance is unknown but the sample size is large (>30). The test
statistics is: z = (46.3-45)/(4.5/ (sqrt (81)) = 2.60. Decision rule: reject H0
if z(computed)>z(critical). Therefore, reject the null hypothesis because
the computed test statistics of 2.60 exceeds the critical z-value of 2.33.
C is incorrect
because z-test (instead of t-test) should be used for sample size (81) ≥30.
D is incorrect
because z-test (instead of t-test) should be used for sample size (81)≤30.
不是说数量都是双尾？VaR都是单尾？这道题就是单尾。
还是说只要提到置信区间或置信度
比如95%confidence interval 或95% level就是双尾
提到significant level就是单位？
