题目
An analyst is examining a large sample with an unknown population variance. Which of the following is the most appropriate test to test the hypothesis that the historical average return on an index is less than or equal to 6%?
选项
A.One-tailed t-test
B.Two-tailed t-test
C.One-sided chi-square test
答案
A
解析
A is correct. If the population sampled has unknown variance and the sample is large, a z-test may be used. Hypotheses involving “greater than” or “less than” postulations are one sided (one tailed). In this situation, the null and alternative hypotheses are stated as H0: μ ≤ 6% and Ha: μ > 6%, respectively. A one-tailed t-test is also acceptable in this case, and the rejection region is on the right side of the distribution. ： A正确。 如果抽样的总体方差未知且样本较大，则可采用z检验。涉及“大于”或“小于”假设的假设是单面的(单侧的)。在这种情况下，原假设和备择假分别是Ho：μ≤6%和Ha：μ> 6%。单尾t检验在这种情况下也是可以接受的。