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The table shows the shipping costs for items of different values.

Shipping Costs for Items
\begin{tabular}{|c|c|}
\hline Total cost of items & Shipping cost \\
\hline [tex]$\$[/tex] 25[tex]$ & $[/tex]\[tex]$ 5.99$[/tex] \\
\hline [tex]$\$[/tex] 45[tex]$ & $[/tex]\[tex]$ 8.99$[/tex] \\
\hline [tex]$\$[/tex] 50[tex]$ & $[/tex]\[tex]$ 8.99$[/tex] \\
\hline [tex]$\$[/tex] 70[tex]$ & $[/tex]\[tex]$ 10.99$[/tex] \\
\hline
\end{tabular}

Which best describes the strength of the correlation?

A. A weak positive correlation
B. A strong positive correlation
C. A weak negative correlation
D. A strong negative correlation

Sagot :

GinnyAnsweridn
To determine the correlation between the total cost of items and the shipping cost, we first need to calculate the correlation coefficient. The correlation coefficient measures the strength and direction of a linear relationship between two variables. It ranges from -1 to 1, where:

- A correlation coefficient close to 1 indicates a strong positive correlation.
- A correlation coefficient close to -1 indicates a strong negative correlation.
- A correlation coefficient close to 0 indicates a weak or no linear correlation.

The given data points are:
- Total cost of items: [tex]$25, $[/tex]45, [tex]$50, $[/tex]70
- Shipping cost: [tex]$5.99, $[/tex]8.99, [tex]$8.99, $[/tex]10.99

Using statistical methods, we calculate the correlation coefficient for these data sets. The calculated correlation coefficient is [tex]\(0.9840915378915647\)[/tex].

Now, let's interpret this result:
- Since the correlation coefficient is [tex]\(0.984\)[/tex], which is very close to [tex]\(1\)[/tex], it indicates a very strong positive correlation.

Therefore, the best description of the relationship between the total cost of items and the shipping cost is:

a strong positive correlation
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