A humane society claims that less than 71% of households in a certain country own a pet. In a random sample of 500 households in that country, 335 say they own a pet. At $\alpha = 0.10$, is there enough evidence to support the society's claim? Complete parts (a) through (c) below.
(a) Identify the claim and state $H_0$ and $H_a$
Identify the claim in this scenario. Select the correct choice below and fill in the answer box to complete your choice.
(Type an integer or a decimal. Do not round.)
A. Less than $\boxed{71}$% of households in the country own a pet.
B. The percentage households in the country that own a pet is not $\boxed{71}$%.
C. More than $\boxed{71}$% of households in the country own a pet.
D. $\boxed{71}$% of households in the country own a pet.
Let $p$ be the population proportion of successes, where a success is a household in the country that owns a pet. State $H_0$ and $H_a$. Select the correct choice below and fill in the answer boxes to complete your choice.
(Round to two decimal places as needed.)
A. $H_0: p = \boxed{0.71}$
$H_a: p \ne \boxed{0.71}$
B. $H_0: p \le \boxed{0.71}$
$H_a: p > \boxed{0.71}$
C. $H_0: p = \boxed{0.71}$
$H_a: p < \boxed{0.71}$
D. $H_0: p < \boxed{0.71}$
$H_a: p \ge \boxed{0.71}$
E. $H_0: p > \boxed{0.71}$
$H_a: p \le \boxed{0.71}$
F. $H_0: p \ge \boxed{0.71}$
$H_a: p < \boxed{0.71}$
(b) Use technology to find the P-value.
Identify the standardized test statistic.
$z = \boxed{}$
(Round to two decimal places as needed.)
Identify the P-value.
$P = \boxed{}$
(Round to three decimal places as needed.)
(c) Decide whether to reject or fail to reject the null hypothesis and interpret the decision in the context of the original claim.
$\boxed{}$ the null hypothesis. There $\boxed{}$ enough evidence to $\boxed{}$ the society's claim.