Jeffrey, as an eight$-$year old, established a mean time of $16\mathrm{.}43$ seconds for swimming the $25-$yard freestyle, with a standard deviation of $0\mathrm{.}8$ seconds. His dad, Frank, thought that Jeffrey could swim the $25-$yard freestyle faster using goggles. Frank bought Jeffrey a new pair of expensive goggles and timed Jeffrey for $1525-$yard freestyle swims. For the $15$ swims, Jeffrey's mean time was $16$ seconds. Frank thought that the goggles helped Jeffrey to swim faster than the $16\mathrm{.}43$ seconds. Conduct a hypothesis test using a preset $\backslash$alpha $=0\mathrm{.}05.$ Assume that the swim times for the $25-$yard freestyle are normal. A$)$ Calculate the z$-$score and p value.$($In a pyhton code$)$