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 12,735 homes $$ 578 \% $$ 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 0.102 (Type an integer or a decimal Do not round.) b. Identify the null and alternative hypotheses. $$ \mathrm{H}_{0} $$ $$ \square $$ $$ \square $$ $$ \square $$ $$ \mathrm{H}_{1} $$ $$ \square $$ $$ \square $$ (Type integers or decimals. Do not round.)

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**(a) Expressing the original claim in symbolic form**

Let $$ p $$ represent the true proportion of homes that have only a landline telephone and no wireless phone. The claim "Fewer than $$ 10.2\% $$ of homes have only a landline telephone and no wireless phone" can be written symbolically as:  
$$
p < 0.102
$$

**(b) Stating the null and alternative hypotheses**

When testing this claim, the null hypothesis is set to reflect no change or the opposite of the alternative claim. Thus, we have:
- Null hypothesis:  
$$
H_0: p \ge 0.102
$$
- Alternative hypothesis:  
$$
H_1: p < 0.102
$$
**(a) Symbolic Form of the Claim** Let $$ p $$ represent the proportion of homes with only a landline telephone and no wireless phone. The claim can be written as: $$ p < 0.102 $$ **(b) Hypotheses** - **Null Hypothesis ($$ H_0 $$)**: $$ H_0: p \ge 0.102 $$ - **Alternative Hypothesis ($$ H_1 $$)**: $$ H_1: p < 0.102 $$

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