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The data for shoe print lengths, foot lengths, and heights of males is recorded.

A two-dimensional plot based on a paired data plotted with reference to two axes is called a scatterplot.

Steps to sketch a scatterplot:

1. Mark horizontal axis for shoe print lengthand vertical axis for the height of males.
2. Mark points for the paired observations corresponding to both axes.

The resultant graph is the scatterplot.

The formula for the correlation coefficient is

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

Let shoe print be defined by variable x and the height of males be defined by variable y.

The valuesare listed in the table below:

Substitute the values in the formula:

\(\begin{aligned} r &= \frac{{5\left( {26649.69} \right) - \left( {150.2} \right)\left( {886.5} \right)}}{{\sqrt {5\left( {157271.5} \right) - {{\left( {150.2} \right)}^2}} \sqrt {5\left( {4523.14} \right) - {{\left( {886.5} \right)}^2}} }}\\ &= 0.591\end{aligned}\)

Thus, the correlation coefficient is 0.591.

Define\(\rho \)as the actual value of the correlation coefficient for shoe print length and the height of males.

For testing the claim, form the hypotheses:

\(\begin{array}{l}{{\rm{H}}_{\rm{o}}}:\rho = 0\\{{\rm{{\rm H}}}_{\rm{a}}}:\rho \ne 0\end{array}\)

The samplesize is 5 (n).

The test statistic is computed as follows:

\(\begin{aligned} t &= \frac{r}{{\sqrt {\frac{{1 - {r^2}}}{{n - 2}}} }}\\ = \frac{{0.591}}{{\sqrt {\frac{{1 - {{0.591}^2}}}{{5 - 2}}} }}\\ &= 1.27\end{aligned}\)

Thus, the test statistic is 1.270.

The degree of freedom is

\(\begin{aligned} df &= n - 2\\ &= 5 - 2\\ &= 3.\end{aligned}\)

Thep-value is computed from the t-distribution table.

\(\begin{aligned} p{\rm{ - value}} &= 2P\left( {T > t} \right)\\ &= 2P\left( {T > 1.27} \right)\\ &= 2\left( {1 - P\left( {T < 1.27} \right)} \right)\\ &= 0.294\end{aligned}\)

Thus, the p-value is 0.294.

Since the p-value is greater than 0.05, the null hypothesis fails to berejected.

Therefore, there is not enough evidence to conclude that the variables shoe print length and height have a linear correlation between them.

Since the two variables are not linearly correlated to one other, one variable cannot be used to estimate the other.

Also, the scatterplot reveals no specific pattern between shoe print length and height of men (linear or non-linear).Thus, the two variables are not associated with one other.