A shoe salesman wants to see if his female customers have a preference in the colour of shoe purchased. What is the test statistici for the following data?
$\begin{array} { l l l l l } \text { Black } & \text { Brown } & \text { Red } & \text { Navy } & \text { White } \ 48 & 32 & 13 & 18 & 23 \end{array}$
A) 28.31
B) 16.77
C) 26.80
D) 21.50

Question

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 25 (since there are 120 customers in total and 5 categories).Therefore, the chi-square test statistic is:$$\chi^2 = \frac{(48 - 25)^2}{25} + \frac{(32 - 25)^2}{25} + \frac{(13 - 25)^2}{25} + \frac{(18 - 25)^2}{25} + \frac{(23 - 25)^2}{25} = 28.31$$Therefore, the correct answer is A) 28.31.

A Shoe Salesman Wants to See If His Female Customers