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

question 50

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?

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Definitions:

Isocost Line

A line that represents all combinations of inputs which have the same total cost.

Capital

Wealth in the form of money or other assets owned by a person or organization or available for purposes such as starting a company or investing.

Labor

Pertains to the utilization of human labor, encompassing both physical and intellectual efforts, in the creation of products and services.

Marginal Rate

Often referred to in the context of taxes or production, indicating the rate of increase or the additional cost or benefit of producing one more unit of a good.