91影视

The data for the direction of kicks and the goalkeeper鈥檚 jump is recorded.

The level of significance is 0.05.

Theexpected frequencyis computed as,

\(E = \frac{{\left( {{\rm{row}}\;{\rm{total}}} \right)\left( {{\rm{column}}\;{\rm{total}}} \right)}}{{\left( {{\rm{grand}}\;{\rm{total}}} \right)}}\)

The table with row and column total is represented as,

Theexpected frequency tableis represented as,

All the expected frequencies are above 5, and hence the requirement for the test is met assuming the sampling is done randomly.

To test the independence of kick direction on goalkeeper鈥檚 jump, the hypothesis is formulated as follows:

\({H_0}:\)The direction of the kick is independent of the direction of the goalkeeper jump.

\({H_1}:\)The direction of the kick is dependent of the direction of the goalkeeper jump.

The value of the test statisticis computed as,

\[\begin{aligned}{c}{\chi ^2} = \sum {\frac{{{{\left( {O - E} \right)}^2}}}{E}} \\ = \frac{{{{\left( {54 - 45.3566} \right)}^2}}}{{45.3566}} + \frac{{{{\left( {1 - 5.7902} \right)}^2}}}{{5.7902}} + ... + \frac{{{{\left( {59 - 49.7343} \right)}^2}}}{{49.7343}}\\ = 14.5887\\ \approx 14.589\end{aligned}\]

Therefore, the value of the test statistic is 14.589.

The degrees of freedomare computed as,

\(\begin{aligned}{c}\left( {r - 1} \right)\left( {c - 1} \right) = \left( {3 - 1} \right)\left( {3 - 1} \right)\\ = 4\end{aligned}\)

Therefore, the degrees of freedom are 4.

From chi-square table, the critical value for row corresponding to 4 degrees of freedom and at 0.05 level of significance 9.488.

Therefore, the critical value is 9.488.

Also, the p-value is computed as 0.0056

Since the critical (9.488) is less than the value of test statistic (14.589), in this case, the null hypothesis is rejected.

Therefore, the decision is to reject the null hypothesis.

There isnot sufficient evidence to favour the claimthatthe direction of the kick is independent of the direction of the goalkeeper jump.

Therefore, the result is supportive of the theory that the direction of kicks is dependent to jumps of goalkeeper.