Two Means - Unknown, Unequal Variance: Videos & Practice Problems

The Mann-Whitney $U$ test is a nonparametric test used to compare two independent samples. It is equivalent to the Wilcoxon rank-sum test and leads to the same conclusions when applied appropriately. The test statistic is calculated as:
$z=\frac{U-\frac{n_1{n}_2}{2}}{\sqrt{\frac{n_1{n}_2(n_1+n_2+1)}{12}}}$
where:
$U=n_1{n}_2+\frac{n_1(n_1+1)}{2}-R$
$n_1=$ size of Sample $1$
$n_2=$ size of Sample $2$
$R=$sum of the ranks for Sample $1$
Use the following pulse rate data (in units of beats per minute) for two groups of athletes to calculate the $z$-test statistic for the Mann-Whitney $U$ test.
Sample $1$ (athletes) : $72,78,80,85,90$
Sample $2$ (long-distance runners): $60,65,68,70,75$