Perform the Indicated Goodness-Of-Fit Test Using the P-Value Method A Random Sample of 325 Military Personnel Currently on Active

Essay

Perform the indicated goodness-of-fit test using the P-value method. Be sure to state the hypotheses and the significancelevel , to compute the value of the test statistic, to obtain the P-value, and to state your conclusion.
-The U.S. Department of Defense provides data on the distribution of military personnel on active duty by branch of service. Below is a table giving the percentage distribution for 1985.
$\begin{array} { l c } \text { Branch of Service } & \text { Percentage } \\\text { Army } & 36.3 \\\text { Navy } & 26.5 \\\text { Marine Corps } & 9.2 \\\text { Air Force } & 28.0\end{array}$

A random sample of 325 military personnel currently on active duty gave the following statistics. $\begin{array} { l c } \text { Branch of Service } & \text { Frequency } \\ \text { Army } & 102 \\\text { Navy } & 101 \\\text { Marine Corps } & 40 \\\text { Air Force } & 82\end{array}$
At the 5% significance level, do the data provide evidence that the current distribution of military personnel on active duty differs from the 1985 distribution?