A coffeehouse wishes to see if customers have any preference among 5 different brands of coffee. A sample of 200 customers provided the data below. Calculate the chi-square test statistic $\chi ^ { 2 }$ used to test the claim that the probabilities show no preference.
$\begin{array}{l|ccccc}
\text { Brand } & 1 & 2 & 3 & 4 & 5 \
\hline \text { Customers } & 55 & 65 & 18 & 30 & 32
\end{array}$

A) $37.45$
B) $48.91$
C) $55.63$
D) $45.91$

Question

A coffeehouse wishes to see if customers have any preference among 5 different brands of coffee. A sample of 200 customers provided the data below. Calculate the chi-square test statistic $\chi ^ { 2 }$ used to test the claim that the probabilities show no preference.
$\begin{array}{l|ccccc}
\text { Brand } & 1 & 2 & 3 & 4 & 5 \
\hline \text { Customers } & 55 & 65 & 18 & 30 & 32
\end{array}$

A) $37.45$
B) $48.91$
C) $55.63$
D) $45.91$

Quizplus · Accepted Answer

The expected frequency for each brand is 40 (since 200 customers / 5 brands = 40). The chi-square statistic is calculated as $\sum \frac{(O_i - E_i)^2}{E_i}$, where $O_i$ is the observed frequency and $E_i$ is the expected frequency. Calculating for each brand: $\frac{(55-40)^2}{40} + \frac{(65-40)^2}{40} + \frac{(18-40)^2}{40} + \frac{(30-40)^2}{40} + \frac{(32-40)^2}{40} = 37.45$.

A Coffeehouse Wishes to See If Customers Have Any Preference χ2\chi ^ { 2 }χ2

A Coffeehouse Wishes to See If Customers Have Any Preference $\chi ^ { 2 }$