When testing whether the correlation coefficient differs from zero,the value of the test statistic is with a corresponding p-value of 0.0653.At the 5% significance level,can you conclude that the correlation coefficient differs from zero?
A)Yes,since the p-value exceeds 0.05.
B)Yes,since the test statistic value of 1.95 exceeds 0.05.
C)No,since the p-value exceeds 0.05.
D)No,since the test statistic value of 1.95 exceeds 0.05.

Question

When testing whether the correlation coefficient differs from zero,the value of the test statistic is  with a corresponding p-value of 0.0653.At the 5% significance level,can you conclude that the correlation coefficient differs from zero?
A)Yes,since the p-value exceeds 0.05. 
B)Yes,since the test statistic value of 1.95 exceeds 0.05. 
C)No,since the p-value exceeds 0.05. 
D)No,since the test statistic value of 1.95 exceeds 0.05.

Quizplus · Accepted Answer

The appropriate null hypothesis for testing whether the correlation coefficient differs from zero is:
H0: p=0
The alternative hypothesis is:
Ha: p≠0
The test statistic value is given as 11eaa4ae_7a90_6771_9180_b769347e9da3_TB2339_11, but we are not given the degrees of freedom or the distribution of the test statistic. Therefore, we cannot compare this value directly to the 5% significance level or to a critical value from a distribution. Instead, we use the p-value of 0.0653 to make our conclusion. Since the p-value is greater than 0.05, we fail to reject the null hypothesis. This means we do not have enough evidence to conclude that the correlation coefficient differs from zero at the 5% significance level. Therefore, the correct answer is C.

When Testing Whether the Correlation Coefficient Differs from Zero,the Value