Has the introduction of more music download services changed the number of university students that download music for free from the internet? Two years ago,approximately 50,000 university students admitted to downloading music for free from the internet.

A) ${\mathrm{H}}_0$ : ? = 50,000 ${\mathrm{H}}_{\mathrm{A}}$ : ? ? 50,000
B) ${\mathrm{H}}_0$ : ? < 50,000 ${\mathrm{H}}_{\mathrm{A}}$ : ? = 50,000
C) ${\mathrm{H}}_0$ : ? > 50,000 ${\mathrm{H}}_{\mathrm{A}}$ : ? = 50,000
D) ${\mathrm{H}}_0$ : ? = 50,000 ${\mathrm{H}}_{\mathrm{A}}$ : ? < 50,000
E) ${\mathrm{H}}_0$ : ? = 50,000 ${\mathrm{H}}_{\mathrm{A}}$ : ? > 50,000

The null hypothesis ( ${\mathrm{H}}_0$ ) typically represents no change or the status quo, in this case, that the mean number of students downloading music for free remains the same ( $\mu =50,000$ ). The alternative hypothesis ( ${\mathrm{H}}_{\mathrm{A}}$ ) suggests there is a change, which could be either an increase or decrease in the number of students downloading music for free ( $\mu \ne 50,000$ ). This is a two-tailed test because it considers both possibilities of the mean being either less than or greater than 50,000.