On the SAT exam, a total of $25$ minutes is allotted for students to answer $20$ math questions without the use of a calculator. A guidance counselor would like to know if the students in his school are prepared to complete this portion of the exam in the time allotted. To investigate, the counselor selects a random sample of $35$ students and administers this portion of the test. The students are instructed to turn in their test as soon as they have completed the questions. The mean amount of time taken by the students is $23\mathrm{.}5$ minutes with a standard deviation of $4\mathrm{.}8$ minutes. The counselor would like to know if the data provide convincing evidence that the true mean amount of time needed for all students of this school to complete this portion of the test is less than $25$ minutes. What are the appropriate hypotheses?

H$0$: $\backslash$mu $=23\mathrm{.}5$ versus Ha: $\backslash$mu $<23\mathrm{.}5,$ where $\backslash$mu $=$ the true mean amount of time needed for students of this school to complete this portion of the exam

H$0$: $\backslash$mu $=23\mathrm{.}5$ versus Ha: $\backslash$mu $>23\mathrm{.}5,$ where $\backslash$mu $=$ the true mean amount of time needed for students of this school to complete this portion of the exam

H$0$: $\backslash$mu $=25$ versus Ha: $\backslash$mu $<25,$ where $\backslash$mu $=$ the true mean amount of time needed for students of this school to complete this portion of the exam

H$0$: $\backslash$mu $=25$ versus Ha: $\backslash$mu $>25,$ where $\backslash$mu $=$ the true mean amount of time needed for students of this school to complete this portion of the exam