91影视

The data for the states and the position of car plates is given.

Compute theexpected frequencyusing the row and columns totals of the observed values,

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

The table for observed values and the respective row and column total is represented as,

Theexpected frequency tableis represented as,

Assume that each subject is randomly selected along with the fact that each expected frequency is greater than 5.

Then, the requirements for the test are satisfied.

The hypotheses are formulated as,

\({H_0}:\)The state and whether a car has front and rear license plates are independent.

\({H_1}:\)The state and whether a car has front and rear license plates are dependent.

The value of the test statisticis computed as,

\(\begin{aligned}{c}{\chi ^2} = \sum {\frac{{{{\left( {O - E} \right)}^2}}}{E}} \\ = \frac{{{{\left( {35 - 34.628} \right)}^2}}}{{34.628}} + \frac{{{{\left( {45 - 20.543} \right)}^2}}}{{20.543}} + ... + \frac{{{{\left( {541 - 516.171} \right)}^2}}}{{516.171}}\\ = 50.4458\end{aligned}\)

Therefore, the value of the test statistic is 50.4458.

The degrees of freedomare computed as,

\(\begin{aligned}{c}\left( {r - 1} \right)\left( {c - 1} \right) = \left( {2 - 1} \right)\left( {3 - 1} \right)\\ = 2\end{aligned}\)

Therefore, the degrees of freedom are 2.

From the chi-square table, the critical value corresponding to 2 degrees of freedom and at 0.05 level of significance 5.992.

Therefore, the critical value is 5.992.

The p-value is obtained as 0.000.

Since the critical value (5.992) is less than the value of the test statistic (50.4458). In this case, the null hypothesis is rejected.

Therefore, the decision is to reject the null hypothesis.

There is insufficient evidence to support the claimthat the state and whether a car has front and rear license plates are independent.

Thus, the execution of rules for license plates is dependent on the states.

The proportion of cars in the study that followed the law of license plate, both front and rear of the car.

Of the three states, all appear to follow the rule by different rates.