Determine whether a correlation coefficient of r = 0.091 is significant at the 5% level for a sample
Size of 120.
A)r is significant at 5%.
B)r is not significant at 5%.

Question

Quizplus · Accepted Answer

To determine the significance of the correlation coefficient, we need to compare it with the critical value of the correlation coefficient at the 5% significance level for a sample size of 120. Using a table or calculator, we find that the critical value is approximately ±0.196. Since the calculated correlation coefficient (r = 0.091) is less than the critical value, we can conclude that it is not significant at the 5% level. Therefore, the answer is B. To determine if a correlation coefficient is significant at a certain level, we need to use a significance test. The null hypothesis for a significance test of a correlation coefficient is that there is no relationship between the two variables in the population (i.e., the true correlation coefficient is zero).

To conduct the significance test, we need to calculate the t-statistic using the following formula:

t = r * sqrt(n-2) / sqrt(1-r^2)

where r is the sample correlation coefficient, n is the sample size, and sqrt() means "take the square root of."

In this case, r = 0.091 and n = 120, so

t = 0.091 * sqrt(120-2) / sqrt(1-0.091^2) = 0.958

To determine if this t-value is significant at the 5% level, we need to compare it to the critical t-value with 118 degrees of freedom (df = n-2) and a significance level of 0.05. Using a t-table or a calculator, we find that the critical t-value is 1.980.

Since our calculated t-value (0.958) is less than the critical t-value (1.980), we fail to reject the null hypothesis. That means we do not have enough evidence to say that there is a significant correlation between the two variables in the population.

Therefore, the correct answer is B: r is not significant at 5%.

Determine Whether a Correlation Coefficient of R = 0