Perform the Indicated Goodness-Of-Fit Test $\text { A random sample of } 448 \text { engines from the firm's Ohio plant gives the following results. }$

question 10

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.
-A firm that manufactures engines for racing boats gathers data from all of its plants. The table below gives the distribution of the life span of the engines (in numbers of months)for the entire firm.
$\begin{array}{lc}\text { Months } & \text { Relative Frequency } \\ \text { Under } 60 & 0.017 \\70-79 & 0.201 \\80-89 & 0.353 \\90-99 & 0.331 \\100-109 & 0.098\end{array}$

$\text { A random sample of } 448 \text { engines from the firm's Ohio plant gives the following results. }$ $\begin{array} { l r } \text { Months } & \text { Number of engines } \\ \text { Under } 60 & 22 \\70 - 79 & 131 \\80 - 89 & 46 \\90 - 99 & 154 \\100 - 109 & 95\end{array}$
At the 5% significance level, do the data provide evidence that the distribution of the life spans of the engines manufactured at the Ohio plant is different from the firm's overall distribution?

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Definitions:

Joseph Brant

A prominent Mohawk military and political leader in the 18th century who was closely associated with Great Britain during the American Revolutionary War.

Hessians

German mercenary soldiers hired by the British Crown to fight against the American colonial forces during the Revolutionary War.

Sovereign Nation

A political entity that possesses autonomy and independence, recognized by other states as having control over its territory and government.

Bunker Hill

A key early battle in the American Revolutionary War notable for the phrase "Don't fire until you see the whites of their eyes," demonstrating colonial forces could stand up to British regulars.