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Sagot :
The amount or level of relationship between the tickets in the bags is
described by the correlation coefficient.
Response:
- The correlation coefficient, r is approximately 0.75
Method by which the correlation coefficient is obtained
Required:
Based on a similar question online, the value of the correlation coefficient, r, is to be determined.
The table of values is presented as follows;
[tex]\begin{tabular}{c|c|c|}\underline{Draw}& \underline{ Bag 1}& \underline{Bag 2}\\Draw 1&2&4\\Draw 2&4&5\\Draw 3 &1&3\\Draw 4&6&4\\Draw 5&7&9\end{array}\right][/tex]
The mean of the first bag, [tex]\overline{x}_1[/tex] = 4
Standard deviation of the first bag, s₁ = 2.5
Mean of the second bag, [tex]\mathbf{\overline x_2}[/tex] = 5
Standard deviation of the second bag, s₂ = 2.3
The sample size from each bag, n = 5
The given regression formula is presented as follows;
[tex]\displaystyle r = \mathbf{ \frac{1}{n - 1} \cdot \sum \left(\frac{x - \overline x}{s_x} \right) \cdot \left(\frac{y - \overline{y}}{s_y} \right)}[/tex]
By calculation using the above data in the table on MS Excel, we have;
[tex]\overline x_1[/tex] = 4, s₁ = 2.54951
[tex]\overline x_2[/tex] = 5, s₂ = 2.345208
The following table of values can be calculated;
[tex]\begin{array}{|c|c|c|c|}&\dfrac{x - \overline x_i}{s_x} & \dfrac{y - \overline y_i}{s_y} & \left(\dfrac{x - \overline x_i}{s_x} \right)\times \left(\dfrac{y - \overline y_i}{s_y} \right) \\&&& \\i = 1&-0.78446&-0.4264&0.334497\\i = 2&0&0&0\\i = 3&-1.1767&-0.8528&1.00349\\i = 4 &0.784464&-0.4264&-0.3345\\i = 5&1.176697&1.705606&\underline{2.006981}\\&&&\\ \ \sum ()&&&3.010471\end{array}\right][/tex]
Therefore;
[tex]\displaystyle \sum \left(\frac{x - \overline x}{s_x} \right) \cdot \left(\frac{y - \overline{y}}{s_y} \right) = \mathbf{ 3.010471}[/tex]
[tex]\displaystyle r = \frac{1}{5-1} \times 3.010471 = 0.752618[/tex]
Rounding off to the nearest hundredth, we have;
- The correlation coefficient, r ≈ 0.75
Possible question options are;
- 0.56
- 0.50
- 0.70
- 0.75
Learn more about correlation coefficient here:
https://brainly.com/question/14753067
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