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 2
If the true correlation between two variables is zero, then which of the following statements is true?
a. There is no linear relationship between the two variables.
b. There may be no relationship between the two variables.
c. Neither There is no linear relationship between the two variables nor There may be no relationship between the two variables.
d. Both There is no linear relationship between the two variables and There may be no relationship between the two variables.
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Table - Correlation Analysis