题目
An analyst is conducting a two-tailed z-test to determine if small cap returns are significantly different from 10%. The sample size is 200 and the computed z-statistic is 2.3. Using a 5% level of significance, which of the following statements is most accurate?
选项
A.Reject the null hypothesis and conclude that small cap returns are not significantly different from 10%.
B.Fail to reject the null hypothesis and conclude that small cap returns are significantly different from 10%.
C.Fail to reject the null hypothesis and conclude that small cap returns are close enough to 10% that we cannot say they are significantly different from 10%.
D.Reject the null hypothesis and conclude that small cap returns are significantly different from 10%.
答案
D
解析
At the 5% level of significance the critical z-statistic for a two-tailed test is 1.96 (assuming a large sample size). The null hypothesis is H0: x = 10%. The alternative hypothesis is Ha: x≠10%. Because the computed z-statistic is greater than the critical z-statistic (2.3>1.96), we reject the null hypothesis and we conclude that small cap returns are significantly different than 10%. 在显着性水平为5％的情况下，两尾检验的临界z统计量为1.96（假设样本量较大）。零假设是 H0：x= 10％。 另一种假设是 Ha：x≠10％。因为计算的z统计量大于临界z统计量（2.3>1.96），所以我们拒绝了原假设，并得出结论：小盘股收益率与10％有显着差异。