A pharmaceutical company has to make a choice between $2$ servers $($A and B$)$ to

run their statistical software programs. $11$ different programs were tested on each

server to determine which server is faster. You can assume that the time to run a

program on each server is normally distributed. Use the R output where needed.

The time $($in seconds$)$ that each server needs to test of a program, is given in the

next table:

Test program Server A Server B

$1233266$

$2264292$

$3233348$

$4181202$

$5226301$

$6210238$

$7230297$

$8250243$

$9215200$

$10234215$

$11282260$

a$.$ The seller of Server A claims that his server needs on average $215$ sec to

execute a program. Construct a $90\%$ confidence interval for the average time

that Server A needs to execute a program. Is the claim of the seller correct?

Explain!