A teacher collected information from a class of 25 students about the time, in hours, they spent studying the previous week and
the time, in hours, they spent on the Internet the previous week. The value of the correlation coefficient between hours spent studying and hours spent on the Internet was −0.72. If the teacher changes the units of each variable from hours to minutes, what will be the value of the correlation coefficient between minutes studying and minutes spent on the Internet?
A. −43.2
B. −0.72
C. −0.012
D. 0.72
E. 60.72
A. −43.2
B. −0.72
C. −0.012
D. 0.72
E. 60.72
1 answer:
Answer:
- <u><em>B. −0.72</em></u>
Explanation:
The <em>correlation coefficient</em> is a measure of the linear association between two variables.
It is a dimensionless value bettween - 1 and +1. Hence, it does not depend on the units that are used to measure the data.
You can see the formula to calculate the correlation coefficient in the attached picture.
There you see that the numerator containts the sum of the differences of the values of the x-variable with its the mean, multiplied by the sum of the differences of the values of the y variable with its mean, while the denominator contains the square root of the product of the squares of the same differences, thus the units are canceled.
In conclusion,<em> If the teacher changes the units of each variable from hours to minutes, the value of the correlation coefficient between minutes studying and minutes spent on the Internet will not change</em>; it will continue being <em>−0.72.</em>
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Answer:
Yes, at a time t such that (√2)/2 ≤ t ≤ 2.
Explanation:
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∴ 1 = 2·t² and from which t = (√2)/2
Hence the function C(x) is decreasing from t = (√2)/2 to t = 2
For Brandon
For 0 ≤ t ≤ 1, 1 ≤ B(t) ≤8 and for 1 < t ≤ 2, 8 < B(t) ≤ 1.5
1 ≤ f(x) ≤ 1.5
Given that the function B(t) is differentiable, therefore, continuous, there exists a point at which the function C(t) and B(t) intersects given that;
For 0 ≤ t ≤ (√2)/2, 0 ≤ C(t) ≤ 23.416 for (√2)/2 < t ≤ 2, 23.416 > C(t) ≥ 2
and for 0 ≤ t ≤ 0 1 ≤ B(t) ≤ 8 and for 1 < t ≤ 2, 8 > B(t) ≥ 1.5
Therefore, the curves intersect at in between (√2)/2 ≤ t ≤ 2.