Notation The author conducted an experiment in which the heigh...

Question

Notation The author conducted an experiment in which the height of each student was measured in centimeters and those heights were matched with the same students’ scores on the first statistics test.
a. For this sample of paired data, what does r represent, and what does represent?

a. For this sample of paired data, what does r represent, and what does represent?

Accepted Answer

All right, hello, everyone. So this question says, a study was conducted where the number of hours students spent studying was recorded and paired with their scores on a mathematics test. In this sample of paired data. What do R and row represent? And here we have 4 different answer choices labeled A through D. Examples of answers proposed. Include relationships between study hours and test scores. Sample correlation coefficient and population correlation coefficient. Probability of getting a high or low score and causation. So first and foremost, what is R? Well, R, if you recall, is the sample. Correlation Coefficient And at this point, it's also worth mentioning that Roe is the population. Correlation coefficient. And the way I remember this is because the letter row looks like a P. So now, let's focus first on R, which is the sample correlation coefficient. Now What it does is measure the strength and direction of the linear relationship between, in this context, study hours and test scores. For the given sample So here, recall that it ranges from -1 to 1. And if R is positive, that is, is greater than 0. That means that there is a positive correlation between the two variables. So this means that both would increase or decrease. So if you have a positive correlation. In this context, that would mean that more study hours leads to higher scores, and conversely, less study hours leads to lower scores. So if one decreases, the other also decreases. Now, here, on the other hand, if R is equal to 0, then there is no correlation between the two variables. And then if R is less than 0, making it negative, that would be a negative correlation. So in a negative correlation, when one variable increases, the other variable would decrease. Now, row, on the other hand, is the correlation coefficient of the population. So here In order to conduct a study, you're taking a sample of people, in this case students, from the greater population. Now here, because you're not studying the entire population. Row cannot be calculated. Instead, it's estimated from the value of R, which represents the sample. Now, if the sample represents the population relatively well, you would get a better estimate of row from R. Therefore, the conclusion corresponds to option B in the multiple choice. Because R represents the sample correlation coefficient, measuring the linear relationship between study hours and test scores in the sample. While Roe is the population correlation coefficient, describing the same relationship for all students. And there you have it. So with that being said, thank you so very much for watching, and I hope you found this helpful.

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