Question

a humane society claims that less than 69% of households in a certain country own a pet. in a random sample of 800 households in that country, 520 say they own a pet. at α = 0.05, is there enough evidence to support the society’s claim? complete parts (a) through (c) below.
z ≈ -2.45
(round to two decimal places as needed.)
identify the p - value.
p ≈ 0.007
(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.
drop - down the null hypothesis. there drop - down enough evidence to drop - down the society’s claim.

Explanation:

Step1: Recall Hypothesis Test Decision Rule

In a hypothesis test, we compare the P - value with the significance level $\alpha$. Here, $\alpha = 0.05$ and the P - value is $P=0.007$. Since $0.007<0.05$, we reject the null hypothesis.

Step2: Interpret the Decision

The null hypothesis in this case is that the proportion of households owning a pet is at least 69% (i.e., $H_0:p\geq0.69$), and the alternative hypothesis (the society's claim) is $H_a:p < 0.69$. Since we reject the null hypothesis, there is enough evidence to support the society's claim.

Answer:

Reject the null hypothesis. There is enough evidence to support the society's claim.