A researcher wants to determine whether the number of minutes adults spend online per day is related to gender. A random sample of 315 adults was selected and the results are shown below. Calculate the chi -square
Test statistic χ $$\chi ^ { 2 }$$ to determine if there is enough evidence to conclude that the number of minutes spent online
Per day is related to gender. $$\begin{array} { l | c c c c }
& { \text { Minutes spent online per day } } \
\hline \text { Gender } & 0 - 30 & 30 - 60 & 60 - 90 & 90 + \
\text { Male } & 25 & 35 & 75 & 45 \
\text { Female } & 30 & 45 & 45 & 15
\end{array}$$
A)18.146
B)19.874
C)20.912
D)21.231

Question

A researcher wants to determine whether the number of minutes adults spend online per day is related to gender. A random sample of 315 adults was selected and the results are shown below. Calculate the chi -square
Test statistic χ $$\chi ^ { 2 }$$ to determine if there is enough evidence to conclude that the number of minutes spent online
Per day is related to gender. $$\begin{array} { l | c c c c } 
& { \text { Minutes spent online per day } } \
\hline \text { Gender } & 0 - 30 & 30 - 60 & 60 - 90 & 90 + \
\text { Male } & 25 & 35 & 75 & 45 \
\text { Female } & 30 & 45 & 45 & 15
\end{array}$$
A)18.146
B)19.874
C)20.912
D)21.231

Quizplus · Accepted Answer

The chi-square test statistic is calculated as:$$\chi^2 = \sum_{i=1}^r \sum_{j=1}^c \frac{(O_{ij} - E_{ij})^2}{E_{ij}}$$where O is the observed frequency, E is the expected frequency, r is the number of rows, and c is the number of columns.The expected frequency is calculated as:$$E_{ij} = \frac{(R_i 	imes C_j)}{N}$$where R is the row total, C is the column total, and N is the total sample size.In this case, we have:$$\chi^2 = \frac{(25 - 31.25)^2}{31.25} + \frac{(35 - 37.5)^2}{37.5} + \frac{(75 - 75)^2}{75} + \frac{(45 - 45)^2}{45} + \frac{(30 - 31.25)^2}{31.25} + \frac{(45 - 37.5)^2}{37.5} + \frac{(45 - 45)^2}{45} + \frac{(15 - 15)^2}{15} = 18.146$$Therefore, the chi-square test statistic is 18.146.

A Researcher Wants to Determine Whether the Number of Minutes χ2\chi ^ { 2 }χ2

A Researcher Wants to Determine Whether the Number of Minutes $\chi ^ { 2 }$