Question

Two bags each contain tickets numbered 1 to 10. John draws a ticket from each bag five times, replacing the tickets after each draw. He records the number on the ticket for each draw from both the bags: Bag 1 Bag 2 Draw 1 2 4 Draw 2 4 5 Draw 3 1 3 Draw 4 6 4 Draw 5 7 9 For the the first bag, the mean is 4 and the standard deviation is 2.5.

Answer 1

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;

$\begin{tabular}{c|c|c|}\underline{Draw}& \underline{ Bag 1}& \underline{Bag 2}\\Draw 1&2&4\\Draw 2&4&5\\Draw 3 &1&3\\Draw 4&6&4\\Draw 5&7&9\end{array}\right]$

The mean of the first bag, $\overline{x}_1$ = 4

Standard deviation of the first bag, s₁ = 2.5

Mean of the second bag, $\mathbf{\overline x_2}$ = 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;

$\displaystyle r = \mathbf{ \frac{1}{n - 1} \cdot \sum \left(\frac{x - \overline x}{s_x} \right) \cdot \left(\frac{y - \overline{y}}{s_y} \right)}$

By calculation using the above data in the table on MS Excel, we have;

$\overline x_1$ = 4, s₁ = 2.54951

$\overline x_2$ = 5, s₂ = 2.345208

The following table of values can be calculated;

$\begin{array}{|c|c|c|c|}&\dfrac{x - \overline x_i}{s_x} & \dfrac{y - \overline y_i}{s_y} & \left(\dfrac{x - \overline x_i}{s_x} \right)\times \left(\dfrac{y - \overline y_i}{s_y} \right) \\&&& \\i = 1&-0.78446&-0.4264&0.334497\\i = 2&0&0&0\\i = 3&-1.1767&-0.8528&1.00349\\i = 4 &0.784464&-0.4264&-0.3345\\i = 5&1.176697&1.705606&\underline{2.006981}\\&&&\\ \ \sum ()&&&3.010471\end{array}\right]$

Therefore;

$\displaystyle \sum \left(\frac{x - \overline x}{s_x} \right) \cdot \left(\frac{y - \overline{y}}{s_y} \right) = \mathbf{ 3.010471}$

$\displaystyle r = \frac{1}{5-1} \times 3.010471 = 0.752618$

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:

brainly.com/question/14753067