Ashland MultiComm Services $($AMS$)$ provides high$-$quality telecommunications services in the Greater Ashland area. AMS traces its roots to a small company that redistributed the broad$-$cast television signals from nearby major metropolitan areas but has evolved into a provider of a wide range of broadband services for residential customers. AMS offers subscription$-$based services for digital cable television, local and long$-$distance telephone services, and high$-$speed Internet access.

Recently, AMS has faced compe$-$tition from other service providers as well as Internet$-$based, on$-$demand streaming services that have caused many customers to "cut the cable" and drop their subscription to cable video services.

The AMS technical services department has embarked on a quality improvement effort. Its first project relates to maintaining the target upload speed for its Internet service subscribers. Upload speeds are measured on a standard scale in which the target value is $1\mathrm{.}0.$

Continuing its monitoring of the upload speed, the technical operations department wants to ensure that the mean target upload speed for all Internet service sub$-$scribers is at least $0\mathrm{.}97$ on a standard scale in which the target value is $1\mathrm{.}0.$ Each day, upload speed was measured $50$ times, with the following results $($Please see the table below$)$

Compute the sample statistics $($mean and standard deviation$)$ and determine whether there is evidence that the population mean upload speed is less than $0\mathrm{.}97$ and write a memo to management that summarizes your conclusions $(10$ points$)$