$[10$ points$].$ Two hundred fifty managers with degrees in business administration indicated their fields of concentration as shown below.

$\backslash$table$[[$Major$,$Top Management,Middle Management,$],[$Management$,65,60,],[$Marketing$,30,20,],[$Accounting$,25,50,],[,,,]]$

$($a$)$ State the null and alternative hypotheses to determine if the position in management is independent of the major of concentration.$[10$ points$].$ Two hundred fifty managers with degrees in business administration indicated their fields of concentration as shown below.

$\backslash$table$[[$Major$,$Top Management,Middle Management,$],[$Management$,65,60,],[$Marketing$,30,20,],[$Accounting$,25,50,],[,,,]]$

$($a$)$ State the null and alternative hypotheses to determine if the position in management is independent of the major of concentration.