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

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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