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Data are provided on the samples of overhead widths (cm) and the weights of seals (kg).

The significance level is 0.05.

Rank correlation coefficient is used to test the significance of the correlation between the two ordinal variables.

The null hypothesis is set up as follows:

There is no correlation between overhead widths and the weights of seals.

\({\rho _s} = 0\)

The alternative hypothesis is set up as follows:

There is a significant correlation between overhead widths and the weight of the seals.

\({\rho _s} \ne 0\)

The test is two tailed.

Here, the data is not given in the form of ranks; so first, determine the ranks of each of the two samples.

Ranks are assigned from the smallest to the largest observations for both samples.

In case some of the values are the same in the sample, the mean of the ranks is assigned to each of the observations.

The following table shows the ranks of the two samples:

Since there are no ties present, the following formula is used to compute the rank correlation coefficient:

\({r_s} = 1 - \frac{{6\sum {{d^2}} }}{{n\left( {{n^2} - 1} \right)}}\)

The following table shows the differences (d) between the ranks of two values for every pair:

Substituting the differences in the formula, the value of\({r_s}\)is obtained as follows:

\(\begin{array}{c}{r_s} = 1 - \frac{{6\sum {{d^2}} }}{{n\left( {{n^2} - 1} \right)}}\\ = 1 - \frac{{6\left( 0 \right)}}{{6\left( {{6^2} - 1} \right)}}\\ = 1\end{array}\)

Therefore, the value of the Spearman rank correlation coefficient is equal to 1.

The critical values of the rank correlation coefficient for n=6 and\(\alpha = 0.05\)are -0.886 and 0.886.

Since the value of the rank correlation coefficient does not fallin the interval bounded by the critical values, the null hypothesis is rejected.

There is enough evidence to conclude that there is a correlation between the overhead width and the weights of the seal.