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 χ $$\chi ^ { 2 }$$ to test the claim that the
Distribution is uniform.. $$\begin{array} { l | c l l l l }
\text { Brand } & 1 & 2 & 3 & 4 & 5 \
\hline \text { Customers } & 30 & 65 & 18 & 32 & 55
\end{array}$$
A)37.45
B)45.91
C)48.91
D)55.63

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 χ $$\chi ^ { 2 }$$ to test the claim that the
Distribution is uniform.. $$\begin{array} { l | c l l l l } 
\text { Brand } & 1 & 2 & 3 & 4 & 5 \
\hline \text { Customers } & 30 & 65 & 18 & 32 & 55
\end{array}$$
A)37.45
B)45.91
C)48.91
D)55.63

Quizplus · Accepted Answer

The chi-square test statistic is calculated as:$$\chi^2 = \sum_{i=1}^k \frac{(O_i - E_i)^2}{E_i}$$where O_i is the observed frequency for category i, E_i is the expected frequency for category i, and k is the number of categories.In this case, the expected frequency for each category is 200/5 = 40. Therefore, the chi-square test statistic is:$$\chi^2 = \frac{(30 - 40)^2}{40} + \frac{(65 - 40)^2}{40} + \frac{(18 - 40)^2}{40} + \frac{(32 - 40)^2}{40} + \frac{(55 - 40)^2}{40} = 37.45$$Therefore, the correct answer is A) 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 $\chi ^ { 2 }$