A sports researcher is interested in determining if there is a relationship between the type of sport and type of team winning (home team versus visiting team). A random sample of 526 games is selected and the results are
Given below. Calculate the chi-square test statistic χ $$\chi ^ { 2 }$$
to test the claim that the type of team winning is
Independent of the sport. $$\begin{array} { l | c c c c }
& \text { Football } & \text { Basketball } & \text { Soccer } & \text { Baseball } \
\hline \text { Home team wins } & 39 & 156 & 25 & 83 \
\text { Visiting team wins } & 31 & 98 & 19 & 75
\end{array}$$
A)3.290
B)2.919
C)5.391
D)4.192

Question

A sports researcher is interested in determining if there is a relationship between the type of sport and type of team winning (home team versus visiting team). A random sample of 526 games is selected and the results are
Given below. Calculate the chi-square test statistic χ $$\chi ^ { 2 }$$
 to test the claim that the type of team winning is
Independent of the sport. $$\begin{array} { l | c c c c } 
& \text { Football } & \text { Basketball } & \text { Soccer } & \text { Baseball } \
\hline \text { Home team wins } & 39 & 156 & 25 & 83 \
\text { Visiting team wins } & 31 & 98 & 19 & 75
\end{array}$$
A)3.290
B)2.919
C)5.391
D)4.192

Quizplus · Accepted Answer

The chi-square test statistic is calculated as:$$\chi^2 = \sum \frac{(O - E)^2}{E}$$where O is the observed frequency and E is the expected frequency.The expected frequency for each cell is calculated as:$$E = \frac{(row \ total) 	imes (column \ total)}{grand \ total}$$The grand total is 526.The row totals are:Football: 39 + 31 = 70Basketball: 156 + 98 = 254Soccer: 25 + 19 = 44Baseball: 83 + 75 = 158The column totals are:Home team wins: 39 + 156 + 25 + 83 = 303Visiting team wins: 31 + 98 + 19 + 75 = 223The expected frequencies are:Football: Home team wins: 70 * 303 / 526 = 41.44Football: Visiting team wins: 70 * 223 / 526 = 28.56Basketball: Home team wins: 254 * 303 / 526 = 149.44Basketball: Visiting team wins: 254 * 223 / 526 = 104.56Soccer: Home team wins: 44 * 303 / 526 = 25.93Soccer: Visiting team wins: 44 * 223 / 526 = 18.07Baseball: Home team wins: 158 * 303 / 526 = 92.64Baseball: Visiting team wins: 158 * 223 / 526 = 65.36The chi-square test statistic is:$$\chi^2 = \frac{(39 - 41.44)^2}{41.44} + \frac{(31 - 28.56)^2}{28.56} + \frac{(156 - 149.44)^2}{149.44} + \frac{(98 - 104.56)^2}{104.56} + \frac{(25 - 25.93)^2}{25.93} + \frac{(19 - 18.07)^2}{18.07} + \frac{(83 - 92.64)^2}{92.64} + \frac{(75 - 65.36)^2}{65.36} = 3.290$$Therefore, the correct answer is A.

A Sports Researcher Is Interested in Determining If There Is χ2\chi ^ { 2 }χ2

A Sports Researcher Is Interested in Determining If There Is $\chi ^ { 2 }$