题目
Which one of the following four statements about hypothesis testing holds true if the level of significance decreases from 5% to 1%?
选项
A.It becomes more difficult to reject a null hypothesis when it is actually true.
B.The probability of making a type I error increases.
C.The probability of making a type II error decreases.
D.The failure to reject the null hypothesis when it is actually false decreases to 1%.
答案
A
解析
Type I error: the rejection of the null hypothesis when it is actually true.Type II error: the failure to reject the null hypothesis when it is actually false.The significance level is the probability of making a type I error.Decreasing the probability level makes it more difficult to reject the null when it is true which means the probability of making a type I error decreases. All else equal, the decrease in the probability of making a type I error comes at the cost of increasing the probability of making a type II error. I类错误：原假设为真时，拒绝原假设。II型错误：在原假设为假时未能拒绝原假设。显着性水平是发生I型错误的概率。降低概率级别会使其更难以拒绝为null的值（这是true时），这意味着发生I型错误的可能性降低。在所有其他条件相同的情况下，降低产生I型错误的可能性的代价是增加产生II型错误的可能性。