Find the Value of the Chi-Square Test Statistic for the Goodness-Of-Fit

Multiple Choice

Find the value of the chi-square test statistic for the goodness-of-fit test.
-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 number of months) for the entire
Firm.
$\begin{array}{r|c}\text { Months } & \text { Relative frequency } \\\hline \text { Under 60 } & 0.078 \\70-79 & 0.205 \\80-89 & 0.491 \\90-99 & 0.151 \\100-109 & 0.075\end{array}$
A random sample of 591 engines from the firm's Ohio plant gives the following results.
$\begin{array}{r|c}\text { Months } & \text { Number of Engines } \\\hline \text { Under } 60 & 105 \\70-79 & 26 \\80-89 & 152 \\90-99 & 182 \\100-109 & 126\end{array}$
You wish to test the claim that the distribution of the life spans of the engines manufactured at the Ohio plant is the same as the firm's overall distribution. What is the value of the $\chi ^ { 2 }$ test statistic?

A) $\chi ^ { 2 } = 52.176$
B) $\chi ^ { 2 } = 427.196$
C) $\chi ^ { 2 } = 107.937$
D) $\chi ^ { 2 } = 462.711$