题目
Jill Batten is analyzing how the returns on the stock of Stellar Energy Corp. are related with the previous month’s percentage change in the US Consumer Price Index for Energy (CPIENG). Based on 248 observations, she has computed the sample correlation between the Stellar and CPIENG variables to be -0.1452. She also wants to determine whether the sample correlation is significantly different from zero. The critical value for the test statistic at the 0.05 level of significance is approximately 1.96. Batten should conclude that the statistical relationship between Stellar and CPIENG is:
选项
A.significant, because the calculated test statistic is outside the bounds of the critical values for the test statistic.
B.significant, because the calculated test statistic has a lower absolute value than the critical value for the test statistic.
C.insignificant, because the calculated test statistic is outside the bounds of the critical values for the test statistic.
答案
A
解析
A is correct. The calculated test statistic is「huixue_img/importSubject/1564548696484483072.png」Because the value of t = －2.30177 is outside the bounds of ±1.96, we reject the null hypothesis of no correlation and conclude that there is enough evidence to indicate that the correlation is different from zero. 计算出检验统计量是： t=[r(n-2)^0.5]/[(1-r^2)]=[-0.1452(248-2)^0.5]/{[(1-(-0.1452)^2)]^0.5}=-2.30177 由于t = -2.30177的绝对值大于1.96，故相关系数具有统计学意义。