Chris Columbus is responsible for controlling inventory levels for four types of sailboats sold by his company. Chris takes a sample of 48 boats sold over the past
Several months to determine if demand is the same for each type. His results are as
Follows: $$\begin{array} { l l }
\text { Type of Boat } & \text { Sales } \
\text { Pirate's Revenge } & 15 \
\text { Jolly Roger } & 11 \
\text { Sails Delight } & 10 \
\text { Cruiser Cove } & 12
\end{array}$$ The calculated value of the Chi Square statistic is
A) 7.815
B) 1.17
C) 22.35
D) -1.17
E) 12.56

Question

Chris Columbus is responsible for controlling inventory levels for four types of sailboats sold by his company. Chris takes a sample of 48 boats sold over the past
Several months to determine if demand is the same for each type. His results are as
Follows: $$\begin{array} { l l } 
\text { Type of Boat } & \text { Sales } \
\text { Pirate's Revenge } & 15 \
\text { Jolly Roger } & 11 \
\text { Sails Delight } & 10 \
\text { Cruiser Cove } & 12
\end{array}$$ The calculated value of the Chi Square statistic is
A) 7.815
B) 1.17
C) 22.35
D) -1.17
E) 12.56

Quizplus · Accepted Answer

The Chi Square statistic is calculated to test whether the observed frequencies (sales of different types of boats) significantly differ from the expected frequencies. In this case, if demand is the same for each type of boat, we would expect each type to have sold the same number, which is the total sales (48) divided by the number of types (4), giving an expected sale of 12 for each type. The Chi Square statistic is calculated using the formula $\chi^2 = \sum \frac{(O_i - E_i)^2}{E_i}$, where $O_i$ is the observed frequency and $E_i$ is the expected frequency. Plugging in the numbers for each type of boat, we get a Chi Square statistic of 1.17, indicating that the difference between the observed and expected sales is not statistically significant at common levels of significance, suggesting that demand might be the same for each type of boat.

Chris Columbus Is Responsible for Controlling Inventory Levels for Four