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 \\(\alpha = 0.05\\), is there enough evidence to support the societys claim? complete parts (a) through (c) below.

(b) use technology to find the p - value.
identify the standardized test statistic.
\\(z = -2.45\\) (round to two decimal places as needed.)
identify the p - value.
\\(p = \square\\) (round to three decimal places as needed.)

Explanation:

Step1: Recognize Test Type

This is a left - tailed z - test for a proportion. The standardized test statistic \(z=- 2.45\).

Step2: Find P - value

For a left - tailed test, the P - value is the probability that \(Z < z\), where \(Z\) follows the standard normal distribution \(N(0,1)\) and \(z=-2.45\). Using a standard normal table or a calculator with a normal distribution function, we calculate \(P(Z < - 2.45)\).
We know that the standard normal distribution is symmetric, so \(P(Z < - 2.45)=1 - P(Z < 2.45)\). Looking up \(P(Z < 2.45)\) in the standard normal table, we find that \(P(Z < 2.45)\approx0.9929\). Then \(P(Z < - 2.45)=1 - 0.9929 = 0.0071\approx0.007\) (rounded to three decimal places).

Answer:

\(0.007\)