25、An analyst conducted a significance test to determine if the relationship between two variables was real or the result of chance. His null hypothesis is that the population correlation coefficient is equal to zero and his alternative hypothesis is that the population correlation coefficient is different from zero. He developed the following information:

Value of the test statistic      2.8092

Critical value at the 0.05 significance level 1.96

Critical value at the 0.01 significance level 2.58

The analyst conducted a:

A. one-tailed test and can reject his null hypothesis.

B. two-tailed test and can reject his null hypothesis.

C. one-tailed test and cannot reject his null hypothesis.

D. two-tailed test and cannot reject his null hypothesis.

答案和详解如下：

25、Correct answer is B

"Hypothesis Testing," Richard A. Defusco, Dennis W. McLeavey, Jerald E. Pinto, and David E. Runkel

2008 Modular Level I, Vol. 1, pp. 456-464

Study Session 3-11-a, c

define a hypothesis, describe the steps of hypothesis testing, interpret and discuss the choice of the null hypothesis and alternative hypothesis, and distinguish between one-tailed and two-tailed tests of hypotheses;

define and interpret a decision rule and the power of a test, and explain the relation between confidence intervals and hypothesis tests

Because the alternative hypothesis is that the correlation is different from zero (either above or below zero), the analyst conducted a two-tailed test. Because the test statistic is greater than either of the critical values, the analyst can reject the null hypothesis.