The amount or level of relationship between the tickets in the bags is
described by the correlation coefficient.
Response:
- The correlation coefficient, <em>r</em> is approximately <u>0.75</u>
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<h3>Method by which the correlation coefficient is obtained</h3>
Required:
Based on a similar question online, the value of the correlation coefficient, <em>r</em>, is to be determined.
The table of values is presented as follows;
![\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]](https://tex.z-dn.net/?f=%5Cbegin%7Btabular%7D%7Bc%7Cc%7Cc%7C%7D%5Cunderline%7BDraw%7D%26%20%5Cunderline%7B%20Bag%201%7D%26%20%5Cunderline%7BBag%202%7D%5C%5CDraw%201%262%264%5C%5CDraw%202%264%265%5C%5CDraw%203%20%261%263%5C%5CDraw%204%266%264%5C%5CDraw%205%267%269%5Cend%7Barray%7D%5Cright%5D)
The mean of the first bag,
= 4
Standard deviation of the first bag, s₁ = 2.5
Mean of the second bag,
= 5
Standard deviation of the second bag, s₂ = 2.3
The sample size from each bag, <em>n</em> = 5
The given regression formula is presented as follows;

By calculation using the above data in the table on MS Excel, we have;
= 4, s₁ = 2.54951
= 5, s₂ = 2.345208
The following table of values can be calculated;
![\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]](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7B%7Cc%7Cc%7Cc%7Cc%7C%7D%26%5Cdfrac%7Bx%20-%20%5Coverline%20x_i%7D%7Bs_x%7D%20%26%20%5Cdfrac%7By%20-%20%5Coverline%20y_i%7D%7Bs_y%7D%20%26%20%5Cleft%28%5Cdfrac%7Bx%20-%20%5Coverline%20x_i%7D%7Bs_x%7D%20%5Cright%29%5Ctimes%20%5Cleft%28%5Cdfrac%7By%20-%20%5Coverline%20y_i%7D%7Bs_y%7D%20%5Cright%29%20%5C%5C%26%26%26%20%5C%5Ci%20%3D%201%26-0.78446%26-0.4264%260.334497%5C%5Ci%20%3D%202%260%260%260%5C%5Ci%20%3D%203%26-1.1767%26-0.8528%261.00349%5C%5Ci%20%3D%204%20%260.784464%26-0.4264%26-0.3345%5C%5Ci%20%3D%205%261.176697%261.705606%26%5Cunderline%7B2.006981%7D%5C%5C%26%26%26%5C%5C%20%5C%20%20%5Csum%20%28%29%26%26%263.010471%5Cend%7Barray%7D%5Cright%5D)
Therefore;


Rounding off to the nearest hundredth, we have;
- The correlation coefficient, r ≈ <u>0.75</u>
<em>Possible question options are;</em>
Learn more about correlation coefficient here:
brainly.com/question/14753067