Police sometimes measure shoe prints at crime scenes so that they can learn something about criminals. Listed below are shoe print​ lengths, foot​ lengths, and heights of males. Construct a​ scatterplot, find the value of the linear correlation coefficient​ r, and find the​ P-value of r. Determine whether there is sufficient evidence to support a claim of linear correlation between the two variables. Based on these​ results, does it appear that police can use a shoe print length to estimate the height of a​ male? Use a significance level of α=0.01

It does not appear that police can use a shoe print length to estimate the height of a​ male.

The given parameters are:

Rewrite as:

See attachment for scatter plot

To determine the correlation coefficient, we extend the table as follows:

The correlation coefficient (r) is:

We have:

Calculate mean of x and y

Calculate SSx and SSy

Calculate

So:

Calculate test statistic:

Calculate the degrees of freedom

The value at:

The value is:

This means that we reject the null hypothesis if the t value is not between -5.841 and 5.841

We calculate the t value as:

Hence, we do not reject the null hypothesis because they do not appear to have any correlation.

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