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

Essay

Perform the indicated goodness-of-fit test. Be sure to state the hypotheses and the significance level, to obtain the criticalvalue, to compute the value of the test statistic, 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.
$\begin{array}{lr} \text { Branch of Service } & \text { Percentage } \\ \text { Army } & 36.3 \\ \text { Navy } & 26.5 \\ \text { Marine Corps } & 9.2 \\ \text { Air Force } & 28.0 \end{array}$
A random sample of 325 military personnel currently on active duty gave the following statistics.
$\begin{array}{lr} \text { Branch of Service } & \text { Frequency } \\ \text { Army } & 118 \\ \text { Navy } & 92 \\ \text { Marine Corps } & 31 \\ \text { Air Force } & 84 \end{array}$
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?