Question

claim: fewer than 10.2% 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 13,190 homes 5.84% 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 10.2% 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 \(p < 0.102\).

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 \(H_0:p = 0.102\) (since the null hypothesis is the opposite of the claim for a one - tailed test in the context of proportion tests, we start with the equality).
• The alternative hypothesis \(H_1:p < 0.102\) (which is the original claim).

Answer:

a. \(p<0.102\)
b. \(H_0:p = 0.102\), \(H_1:p < 0.102\)