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

---

Definitions:

Population

The whole number of people or inhabitants in a country or region, or a specific group of individuals being studied.

Reinforcement

A concept in psychology and behavior analysis where a certain behavior is encouraged or discouraged through rewards or punishments.

Unconditioned Stimulus

In classical conditioning, it is a stimulus that unconditionally, naturally, and automatically triggers a response without prior learning.

Conditioned Stimulus

A previously neutral stimulus that, after becoming associated with an unconditioned stimulus, elicits a conditioned response in classical conditioning.