Suppose that the average waiting time for a patient at a physician's office is just over $29$ minutes Suppose that the average waiting time for a patient at a physician's office is just over $29$ minutes. To

address the issue of long patients', wait times, some physicians' offices are using wait$-$tracking systems

to notify patients of expected wait times. Patients can adjust their arrival times based on this

information and spend less time in waiting rooms. The following data show wait times $($in minutes$)$

for a sample of patients at offices that do not have a wait$-$tracking system and wait times for a sample

of patients at offices with such systems. The data are stored in HI$6007$ Group Assignment T$12024$

data file $($sheet $1).$

a$)$ Calculate the mean and median patient wait times for offices;

i$.$ with a wait$-$tracking system?

ii$.$ without a wait$-$tracking system?

b$)$ Calculate the variance and standard deviation of patient wait times for offices;

i$.$ with a wait$-$tracking system?

ii$.$ without a wait$-$tracking system?

c$)$ Create a box plot for patient wait times for offices;

i$.$ with a wait$-$tracking system and review the information from the box plot?

ii$.$ without a wait$-$tracking system and review the information from the box plot?

d$)$ Do offices with a wait$-$tracking system have shorter patient wait times than offices without a

wait$-$tracking system? Explain.