Question

claim: fewer than 8.2% 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 11,878 homes 5.78% 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.
(type an integer or a decimal. do not round.)
b. identify the null and alternative hypotheses.
(type integers or decimals. do not round.)

Explanation:

Step1: Express the original claim

The claim is "Fewer than 8.2% of homes have only a landline telephone and no wireless phone". Let \(p\) be the proportion of homes that have only a landline telephone and no wireless phone. The symbolic form of the claim is \(p < 0.082\).

Step2: Identify the 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.

• The null hypothesis \(H_0:p = 0.082\)
• The alternative hypothesis \(H_1:p < 0.082\)

Answer:

a. \(p < 0.082\)
b. \(H_0:p = 0.082\), \(H_1:p < 0.082\)