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

question 57

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.
 Branch of Service  Percentage  Army 36.3 Navy 26.5 Marine Corps 9.2 Air Force 28.0\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.  Branch of Service  Frequency  Army 102 Navy 101 Marine Corps 40 Air Force 82\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?

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Definitions:

Error

A mistake or inaccuracy in action, calculation, opinion, or judgment caused by poor reasoning or misunderstanding.

Judgment

The ability to make considered decisions or come to sensible conclusions.

Tendency

An inclination towards a particular type of behavior, action, or thought.

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