Ten pairs of points yielded a correlation coefficient r of 0.79.If which of the following statements is correct if (Do not calculate a t-value.)
A)Because 0.79 is greater than 0.632, the null hypothesis is not rejected.
B)Because 0.79 is greater than 0.632, the null hypothesis is rejected.
C)Because 0.79 is greater than 0.602, the null hypothesis is not rejected.
D)There is no correlation between the variables.

Question

Ten pairs of points yielded a correlation coefficient r of 0.79.If  which of the following statements is correct if  (Do not calculate a t-value.)
A)Because 0.79 is greater than 0.632, the null hypothesis is not rejected. 
B)Because 0.79 is greater than 0.632, the null hypothesis is rejected. 
C)Because 0.79 is greater than 0.602, the null hypothesis is not rejected. 
D)There is no correlation between the variables.

Quizplus · Accepted Answer

Based on the given information, the correlation coefficient between the ten pairs of points is 0.79. Since the sample size is less than 30 and no t-value is given, we cannot calculate the significance level for the correlation coefficient. Instead, we compare the correlation coefficient to a critical value at a 5% significance level for a two-tailed test, which is approximately 0.632 for a sample size of 10.

Since the correlation coefficient of 0.79 is greater than the critical value of 0.632, we reject the null hypothesis and conclude that there is a significant positive correlation between the two variables. Therefore, the correct choice is B. The correlation coefficient r of 0.79 indicates a strong positive correlation between the variables. The critical value for a two-tailed test at a significance level of 0.05 with 10 degrees of freedom is 0.632. Since 0.79 is greater than 0.632, we reject the null hypothesis and conclude that there is a significant correlation between the variables. Therefore, choice B is the correct answer.

Ten Pairs of Points Yielded a Correlation Coefficient R of 0.79.If