Question

claim: fewer than 11.5% of homes have only a landline telephone and no wireless phone. sample data: a survey by the national center for health statistics showed that among 14,653 homes 5.81% had landline phones without wireless phones. complete parts (a) and (b). a. express the original claim in symbolic form. let the parameter represent a value with respect to homes that have only a landline telephone and no wireless phone. p < 0.115 (type an integer or a decimal. do not round.) b. identify the null and alternative hypotheses. h₀: ▼ ▼ □ h₁: ▼ ▼ □ (type integers or decimals. do not round.)

Explanation:

Step1: Recall the concept of null and alternative hypotheses

The null hypothesis \(H_0\) is a statement of equality. The alternative hypothesis \(H_1\) is the claim we are trying to find evidence for.

Step2: Formulate the null and alternative hypotheses

Since the claim is \(p < 0.115\), the null hypothesis is \(H_0:p = 0.115\) (the opposite of the claim in a way that assumes no difference initially). The alternative hypothesis is \(H_1:p < 0.115\) (which is the claim we are testing).

Answer:

\(H_0:p = 0.115\)
\(H_1:p < 0.115\)