The mean work week for data scientists in a start$-$up company is believed to be about $50$ hours. A newly

hired data scientist hopes that the work hours is shorter. She asks ten data scientist friends in similar

start$-$up companies for their usual weekly work hours. Based on the responses $($see below$),$ should she

consider that the mean work week in her new company to be shorter than $50$ hours? Test at $\backslash$alpha $=0\mathrm{.}10.$

Responses: $45,40,55,50,55,45,55,50,40,60.$ Can a t$-$test for a mean be performed here even if the sample was only gathered from friends? Justify the use of the chosen statistical test