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.
b. Without doing any research or calculations, estimate the value of r.

b. Without doing any research or calculations, estimate the value of r.

Accepted Answer

All right. Hello, everyone. So this question says, a researcher conducted an experiment in which he recorded the number of daily exercise minutes for a group of students and matched these values with their scores on a physical fitness test. Without performing any calculations or research, estimate the value of R. In other words, the correlation coefficient. Option A says approximately 0, 0.7. B says approximately 0.0. C says approximately 0.3. And D says approximately 0.8. So let's talk about the correlation coefficient, and specifically what the number tells you. Because recall that the correlation coefficient, that is R, can range from -1 to 1. So here When R is greater than 0, that is when R is positive, that means that there is a positive correlation. A positive linear correlation between the two variables that you're examining. So When it comes to a positive correlation. Right? When one increases, the other variable also increases, and conversely, when one decreases, the other one also decreases. On the other hand, when R is less than 0, making it negative, that means that there's a negative correlation. And so when you have a negative linear correlation, when one variable increases, the other variable decreases. And on the other hand, when R is equal to 0, that means that there is no correlation. Between the two variables that you're examining. So basically, R is about measuring the strength and direction of a linear relationship between two variables, if one exists. So here, in this scenario. If more students, or rather, if students exercise more. And subsequently score higher on the fitness test, that would indicate a positive correlation. If there's no consistent relationship, or would be closer to zero. And If increased exercise minutes actually decreased fitness scores, that would mean a negative correlation. Now, the last scenario is highly unlikely. Because regular exercise is generally considered to be associated with better physical fitness. So, because of that, we would expect to see a moderate to strong positive correlation with the value of R being closer to 1. So generally around 0.6 to 0.9. So therefore, Our answer should be option D, the multiple choice because approximately 0.8 is the most appropriate for this context. 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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