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.
$\begin{array} { l c } \text { Branch of Service } & \text { Percentage } \\\text { Army } & 36.3 \\\text { Navy } & 26.5 \\\text { Marine Corps } & 9.2 \\\text { Air Force } & 28.0\end{array}$

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?

---

Definitions:

Correlational

Correlational research refers to a type of non-experimental study designed to identify the relationship or association between two or more variables, without implying causation.

Statistical Results

Outcomes derived from the application of statistical methods, often used to infer conclusions from data.

Inferential Statistics

Mathematical procedures that allow a researcher to draw further claims from a data pattern, including claims about whether the pattern observed in the sample is likely to be observed in other samples.

Examining Data

The process of analyzing information or facts to draw conclusions or make decisions.