$($In a python code$)$ 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 $15,25-$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 a$=0\mathrm{.}05.$ Assume that the swim times for the $25-$yard freestyle are normal. A$)$ Is this a test about a population mean or proportion? State Hypothesis: Is this a right, left or two tailed test? B$)$ Define the standard deviation, mean $,$ and sample size and create the distribution for the test. C$)$ Calculate Z$-$ Score and P$-$Value D$)$ What is your decision at the preconcieved significance level, and why $($indicate decsion$)?$What is your conclusion, does Jeffrey swim faster in the new goggles?