In the Study "The Role of Sports as a SocialSource: Chase, M

Question

Examlex · Accepted Answer

The Answer is

\mathrm { H } _ { 0 }

: Type of school district and personal school goal are independent.

\mathrm { H } _ { \mathrm { A } }

: There is an association between type of school district and personal school goal.
Conditions:
*Counted Data: We have counts of the number of students in each category.

{ } ^ { * }

Randomization: It is given that the sample was randomly selected.
*Expected Cell Frequency: All expected counts are greater than 5 (shown in parenthesis in the table below), so this condition is satisfied.
Under these conditions, the sampling distribution of the test statistic is

\chi ^ { 2 }

with

( \mathrm { r } - 1 ) ( \mathrm { c } - 1 ) = ( 3 - 1 ) ( 3 - 1 ) = ( 2 ) ( 2 ) = 4

degrees of freedom, and we will perform a

\chi ^ { 2 }

test of independence.

\begin{array}{|l|c|c|c|}\hline & ext { Rural } & ext { Suburban } & ext { Urban } \\hline ext { Make Good Grades } & 57(74.72) & 87(75.73) & 24(17.55) \\hline ext { Be Popular } & 50(43.59) & 42(44.17) & 6(10.24) \\hline ext { Be Good at Sports } & 42(30.69) & 22(31.10) & 5(7.21) \\hline\end{array}

\chi ^ { 2 } = \sum \frac { ( O b s - E x p ) ^ { 2 } } { \operatorname { Exp } } = \frac { ( 57 - 74.72 ) ^ { 2 } } { 74.72 } + \frac { ( 87 - 75.73 ) ^ { 2 } } { 75.73 } + \frac { ( 24 - 17.55 ) ^ { 2 } } { 17.55 } + \ldots + \frac { ( 5 - 7.21 ) ^ { 2 } } { 7.21 }

= 18.564

The

P

-value is

P \left( \chi ^ { 2 } > 18.564 ight) = .000957

.
With this very small

P

-value, we have sufficient evidence to reject the null hypothesis that school district type and personal school goals are independent
variables. The data provide sufficient evidence to support an association between school district type and personal school goal. Students in rural school are much less likely to be concerned with good grades and much more likely to be concerned with being good at sports.

In the Study "The Role of Sports as a Social

Definitions: