4. The sports performance director at a university wishes to investigate whether there is a difference in the means of the specific gravities of blood of cyclists and runners. She models the distribution of specific gravity for cyclists as \(\mathrm { N } \left( \mu _ { X } , 8 ^ { 2 } \right)\) and for runners as \(\mathrm { N } \left( \mu _ { Y } , 10 ^ { 2 } \right)\).

1. State suitable hypotheses for this investigation.
   The mean specific gravity of blood of a random sample of 40 cyclists from the university was 1063. The mean specific gravity of blood of a random sample of 40 runners from the same university was 1060.
2. Calculate and interpret the \(p\)-value for the data.
3. Suppose now that both samples were of size \(n\), instead of 40. Find the least value of \(n\) that would ensure that an observed difference of 3 in the mean specific gravities would be significant at the \(1 \%\) level.