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:

Authoritative Parenting

A parenting style characterized by a high level of demand and responsiveness, where parents set clear standards and limits but are also supportive and responsive to their children's needs.

Permissive

Describing an approach or policy that allows or tolerates behaviors that might be disallowed or controlled in other contexts; often used in reference to parenting or governance styles.

Authoritarian

A leadership or parenting style characterized by strict rules, high demands, and little warmth or feedback given to subordinates or children.

Middle Adulthood

A stage of human development that occurs roughly between the ages of 40 and 65, marked by personal, social, and career transitions.