A study of 20 students showed that the correlation between the time spent writing a test and the number of hours studied the night before the test was 0.35. Using a level of significance equal to 0.05, which of the following statements is true?
A) The sample correlation coefficient could be zero since the test statistic does not fall in the rejection region.
B) The null hypothesis that the population mean is equal to zero should not be rejected, and we should conclude that the true correlation coefficient is zero.
C) There is not enough statistical evidence to conclude that the true correlation coefficient is different from zero.
D) The null hypothesis that the population variance is equal to zero should be rejected, and we should conclude that the true correlation coefficient is zero.
E) None of these.

Question

Quizplus · Accepted Answer

The level of significance is 0.05, which means that the critical value for a two-tailed test with 18 degrees of freedom is 2.101. The test statistic for a correlation coefficient of 0.35 with 18 degrees of freedom is 1.034. Since the test statistic is less than the critical value, we fail to reject the null hypothesis that there is no correlation between the time spent writing a test and the number of hours studied the night before the test. Therefore, there is not enough statistical evidence to conclude that the true correlation coefficient is different from zero.

A Study of 20 Students Showed That the Correlation Between