A study of 20 worldwide financial institutions showed the correlation between their assets and pretax profit to be .86. At the .05 significance level, can we conclude that there is positive correlation in the population?
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Glad to help you out here with the correlation problem. Just a few considerations first with respect to correlation coefficients. In any type of research investigation the task is to determine whether or not there exists any statistically significant difference, effect or relationship (correlation) between and among those variables being studied. When determining correlation we are actually seeking to determine whether or not there exists a relationship between A and B. Correlations range between a perfect negative correlation of -1.0 to a perfect positive correlation between A and B of +1.0. Should a research investigator receive anything beyond these two values then a mistake in the mathematical calculations has been made. However, simply because a correlation coefficient is either positive or negative does not mean the results are statistically significant. To determine whether or not the correlation received is statistically significant the value found must equal or exceed the critical value needed to reject the null hypothesis that no relationship exists. To find out the critical value needed one only has to consult an "r" table in the back of any statistic's book and look up the required critical value needed for either a .05 or .01 confidence or alpha level. If there is statistically significant "r" or correlation value the research investigator can conclude there exists a true relationship between variable A and ...
This solution involves a discussion of the relation between significant and conclusions about correlations.