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

question 28

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) \(\chi ^ { 2 } = 462.711\)

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Definitions:

Monthly Interest Rate

The percentage of interest that is charged or earned on an investment or loan on a monthly basis.

Default Rate

The rate at which borrowers fail to make required payments on their loans or credit obligations.

Monthly Interest Rate

The percentage of interest calculated on a monthly basis typically used in loans and financial products.

EOQ

Economic Order Quantity, an inventory management technique that determines the ideal order size to minimize total inventory costs including holding and ordering costs.