Question

A study of car accidents and drivers who use cellular phones provided the following sample data.

                              Had accident            Had no accident

                        Cellular phone user                     25                                 280

                        Not cellular phone user                48                               412

a) What is the size of the table?

b) At α = 0.01, test the claim that the occurrence of accidents is independent of the use of cellular phones.

Answer 1

a)

It is a 2*2 table

b)

(1) Null and Alternative Hypotheses The following null and alternative hypotheses need to be tested: H0​: The two variables - Occurrence of accidents and Use of cellular phones are independent Ha​: The two variables - Occurrence of accidents and Use of cellular phones are dependent This corresponds to a Chi-Square test of independence. (2) Degrees of Freedom The number of degrees of freedom is df = (2 - 1) * (2 - 1) = 1 (3) Critical value and Rejection Region Based on the information provided, the significance level is α=0.01, the number of degrees of freedom is df = (2 - 1) * (2 - 1) = 1, so the critical value is 6.6349. Then the rejection region for this test becomes R={χ2:χ2>6.6349}. (4)Test Statistics The Chi-Squared statistic is computed as follows: (5)P-value The corresponding p-value for the test is p=Pr(χ2​>1.0642)=0.3023 (6)The decision about the null hypothesis Since it is observed that χ2=1.0642<χ2_c​rit=6.6349, it is then concluded that the null hypothesis is NOT rejected. (7)Conclusion It is concluded that the null hypothesis Ho is NOT rejected. Therefore, there is NOT enough evidence to claim that the two variables - Occurrence of accidents and Use of cellular phones are dependent, at the 0.01 significance level. Conditions: a. The sampling method is simple random sampling. b. The data in the cells should be counts/frequencies c. The levels (or categories) of the variables are mutually exclusive.

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