Final answer:
To potentially achieve a significant correlation coefficient, increasing the sample size is the best approach as it increases the statistical power of the test, providing a more precise estimate of the population correlation coefficient.
Step-by-step explanation:
After calculating a correlation coefficient, you discover that the value is not significant at the 5% level; a common question that arises is what can be done to produce a significant difference. The possible actions include:
- Nothing, the value will remain the same regardless of sample size.
- Increase the sample size: A larger sample size can result in a more precise estimate of the population correlation coefficient and potentially lead to a significant result if the true correlation is not zero.
- Decrease the sample size: This is not typically a viable strategy for achieving significance and may actually decrease the precision of the estimate.
It is important to note that if the p-value is not less than the significance level (a = 0.05), the decision will be not to reject the null hypothesis. The hypothesis test evaluates whether the value of the population correlation coefficient p is close to zero or significantly different from zero using the sample correlation coefficient r and the sample size n. Therefore, if seeking significance, increasing the sample size is the recommended action to increase the statistical power of the test.