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The table represents the time (sec) that has lapsed from the throw and the height (m) of the soccer ball.

Let x represents the Time (sec).

Let y represent the Height (m).

The formula for computing the correlation coefficient (r) between the values of Time (sec) and Height (m) is as follows:

\(r = \frac{{n\sum {xy} - \sum x \sum y }}{{\sqrt {n\sum {{x^2}} - {{\left( {\sum x } \right)}^2}} \sqrt {n\sum {{y^2}} - {{\left( {\sum y } \right)}^2}} }}\)

The following calculations are done to compute the value of r:

Substituting the above values, the value of r is obtained as,

\(\begin{aligned} r &= \frac{{n\sum {xy} - \sum x \sum y }}{{\sqrt {n\sum {{x^2}} - {{\left( {\sum x } \right)}^2}} \sqrt {n\sum {{y^2}} - {{\left( {\sum y } \right)}^2}} }}\\ &= \frac{{10\left( {32.54} \right) - \left( 9 \right)\left( {32} \right)}}{{\sqrt {10\left( {11.4} \right) - {{\left( 9 \right)}^2}} \sqrt {10\left( {123.32} \right) - {{\left( {32} \right)}^2}} }}\\ &= 0.450\end{aligned}\)

Therefore, the value of r is equal to 0.450.

Here, n=10.

If the value of the correlation coefficient lies between the critical values, then the correlation between the two variables is considered significant else, it is considered insignificant.

The critical values of r for n=10 and \(\alpha = 0.05\) are -0.632 and 0.632.

The corresponding p-value of r is equal to 0.192.

Since the computed value of r equal to 0.450 is greater than the larger critical value of 0.192, it can be said that the correlation between the two variables is insignificant.

Moreover, the p-value is greater than 0.05. This also implies that correlation is insignificant.

Therefore, there is not sufficient evidence to claim that there is a linear correlation between the time (sec) and the height (m).