Final answer:
The null hypothesis in a two-way chi-square test of independence states that there is no significant relationship between the two variables, meaning they are considered independent. The correct option for the question is a. true.
Step-by-step explanation:
In a two-way chi-square, also known as a chi-square test of independence, the null hypothesis states that there is no significant relationship between the two variables. This means that the null hypothesis posits that the two factors being studied are independent of each other. In contrast, the alternative hypothesis suggests that there is a significant relationship between the variables, implying that the factors are dependent. When conducting the test, observed values are compared to expected values to determine if there is a significant divergence from what would be expected if the null hypothesis were true. This test is right-tailed and each cell category must have an expected value of at least five to ensure sufficient data for a reliable test.
Drawing from the reference information provided, in context, if we expect about 28 people from the sample to use cell phones while driving and to receive speeding violations, we are examining the relationship between these two factors. Therefore, the correct option for the initial question is a. true. The null hypothesis for a two-way chi-square does indeed state that there is no significant relationship between the two variables being studied.