$4.$ You are the manager of a Project Management Office $($PMO$).$ You receive a proposal for a project with a mean budget of $$2\mathrm{.}5$M$.$ You do not think that this estimate is correct. To validate your assertion, you review archived historical budget documents for $30$ previously completed similar projects in the organization and find the mean budget of the sample of $30$ projects to be $$2\mathrm{.}2$M with a standard deviation of $$700,000.$ Is there enough evidence to support your claim at $\backslash$alpha $=0\mathrm{.}05?$ Use a p$-$value.