Final answer:
The null hypothesis for the claim that less than 57% of people support stricter gun laws is H_0: P ≥ 0.57, and the alternative hypothesis is H_a: P < 0.57. A statistical test would determine if there's enough evidence to reject the null hypothesis.
Step-by-step explanation:
To solve the mathematical problem completely, and to express the null and alternative hypotheses in symbolic form for the claim that less than 57% of people support stricter gun laws, we need to understand the definitions of the null hypothesis (H0) and the alternative hypothesis (Ha). The null hypothesis is a statement that there is no effect or no difference, and it is what we assume to be true until we have evidence to the contrary. The alternative hypothesis is a statement that suggests a potential effect or difference that might be true.
For the given claim, the null hypothesis would be that 57% or more of the population do support stricter gun laws. Symbolically, this can be expressed as:
H0: P ≥ 0.57
The alternative hypothesis would be that less than 57% of the population support stricter gun laws. Symbolically, this can be expressed as:
Ha: P < 0.57
To test these hypotheses, one would collect sample data and perform a statistical test, such as a Z-test for proportions, to determine whether the null hypothesis can be rejected or not, based on an alpha level (typically 0.05) and the calculated p-value from the sample data.