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The table shows the mathematics entrance test scores x and the final examination scores y in an algebra course for a sample of 10 students.
x.....22 29 35 40 44 48 53 58 65 76
y.....53 74 57 66 79 90 76 93 83 99(a) Sketch a scatter plot of the data.
(b) Find the entrance test score of any student with a final exam score in the 80s.
(c) Does a higher entrance test score imply a final exam score? Explain.
Part (a) is just plotting points on the xy-plane.
Part (b)
The entrance score is 65 as shown in the table above for the point (65, 83).
Part (c)
A higher entrance score does not imply a higher final exam score. The table shows how entrance scores and final exam scores fluctuate. The point (76, 99) shows that a high entrance score led to a high final exam score but the case is different for (48, 90). A low entrance score of 48 led to a high final exam score of 90. Many factors lead to this fluctuation in terms of entrance scores versus final exam scores.
To determine if a higher entrance test score implies a higher final exam score, we can examine the scatter plot and observe the general trend of the data points.
In this case, a scatter plot would show the entrance test scores (x-axis) and the final exam scores (y-axis). Based on the given data, we can plot the points as follows:
(x, y)
(22, 53)
(29, 74)
(35, 57)
(40, 66)
(44, 79)
(48, 90)
(53, 76)
(58, 93)
(65, 83)
(76, 99)
By plotting these points, we can visually observe the relationship between the entrance test scores and the final exam scores. If the points generally form an upward trend or positive correlation, it would imply that a higher entrance test score is associated with a higher final exam score.
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