Using statistics $-$ Precast concrete panels are a popular construction material due to their efficiency

and durability. However, concerns exist about the impact of transportation vibrations

on the panels during delivery. engineers suspect that a new type of shock$-$

absorbing material placed between the panels during transport might significantly

reduce these vibrations.

To test the effectiveness of the new shock$-$absorbing material, an engineer randomly

selected $15$ precast concrete panels. He measured the vibration levels $($peak

acceleration$)$ experienced by each panel during a simulated transport journey with

the new material inserted. The table below contines the experment results.

The engineer believes the average peak acceleration experienced by the panels with

the new material will be lower than a specific threshold value $0\mathrm{.}82g(g$ is the

acceleration due to gravity$).$

The engineer wants your herlp in determining if there is evidence $($with $=0\mathrm{.}05)$ to

support a claim that the new shock$-$absorbing material reduces vibration levels $($i$.$e$.,$

lower than a specific threshold value $0\mathrm{.}82g)$