A humane society claims that less than 72% of households in a certain country own a pet. In a random sample of 800 households in that country, 560 say they own a pet. At a = 0.01, is there enough evidence to support the society's claim? Complete parts (a) through (c) below. (a) Identify the claim and state Ho and Ha 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.) OA. % of households in the country own a pet. OB. More than % of households in the country own a pet. OC. The percentage households in the country that own a pet is not %. OD. Less than 72 % 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 Ho and H₂. Select the correct choice below and fill in the answer boxes to complete your choice. (Round to two decimal places as needed.) OC. Ho: P< OA. Ho:p> B. Ho: ps 0.72 H₂:p> 0.72 H₂:pz H₂:ps OF. Ho: p2 OD. Ho: p= H₂: P H₂: p< (b) Use technology to find the P-value. Identify the standardized test statistic. Z= -2.36 OE. Ho: P H₂: p= ‒‒ ‒‒
A humane society claims that less than 72% of households in a certain country own a pet. In a random sample of 800 households in that country, 560 say they own a pet. At a = 0.01, is there enough evidence to support the society's claim? Complete parts (a) through (c) below. (a) Identify the claim and state Ho and Ha 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.) OA. % of households in the country own a pet. OB. More than % of households in the country own a pet. OC. The percentage households in the country that own a pet is not %. OD. Less than 72 % 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 Ho and H₂. Select the correct choice below and fill in the answer boxes to complete your choice. (Round to two decimal places as needed.) OC. Ho: P< OA. Ho:p> B. Ho: ps 0.72 H₂:p> 0.72 H₂:pz H₂:ps OF. Ho: p2 OD. Ho: p= H₂: P H₂: p< (b) Use technology to find the P-value. Identify the standardized test statistic. Z= -2.36 OE. Ho: P H₂: p= ‒‒ ‒‒
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:### Statistical Analysis of Pet Ownership in Households
**Problem Statement:**
A humane society claims that less than 72% of households in a certain country own a pet. In a random sample of 800 households in that country, 560 say they own a pet. At a significance level of α = 0.01, is there enough evidence to support the society's claim?
Complete the following 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.
- \( \Box \) \( % \) of households in the country own a pet.
- \( \Box \) More than \( % \) of households in the country own a pet.
- \( \Box \) The percentage of households in the country that own a pet is not \( % \).
- \( \marked D \) Less than \( 72 \) % 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.)
- \( \Box \) \( H_0 \): \( p > \)
\( H_a \): \( p \leq \)
- \( \marked B \) \( H_0 \): \( p \geq 0.72 \)
\( H_a \): \( p < 0.72 \)
- \( \Box \) \( H_0 \): \( p \ne \)
\( H_a \): \( p = \)
- \( \Box \) \( H_0 \): \( p = \)
\( H_a \): \( p \ne \)
- \( \Box \) \( H_0 \): \( p \leq \)
\( H_a \): \( p > \)
- \( \Box \) \( H_0 \): \( p \geq \)
\( H_a \): \( p < \)
#### (b) Use Technology to Find the P-value.
**Identify the standardized test statistic.**
\[ z
![### Using Technology to Determine the P-Value
**Identify the standardized test statistic.**
The standardized test statistic \( z \) is found to be:
\[ z = -2.36 \]
(Note: The value is rounded to two decimal places as needed.)
**Identify the P-value.**
The P-value corresponding to the test statistic is:
\[ P = 0.0091 \]
(Note: The value is rounded to three decimal places as needed.)
**Decide whether to reject or fail to reject the null hypothesis and interpret the decision in the context of the original claim.**
\[ \text{Reject} \]
The null hypothesis. There **is** enough evidence to **support** the society's claim.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fac4255ba-2787-4b8b-b63d-664d949df058%2Facae6bf0-9326-47ea-9601-ae2334bbdc33%2Foal4psr_processed.png&w=3840&q=75)
Transcribed Image Text:### Using Technology to Determine the P-Value
**Identify the standardized test statistic.**
The standardized test statistic \( z \) is found to be:
\[ z = -2.36 \]
(Note: The value is rounded to two decimal places as needed.)
**Identify the P-value.**
The P-value corresponding to the test statistic is:
\[ P = 0.0091 \]
(Note: The value is rounded to three decimal places as needed.)
**Decide whether to reject or fail to reject the null hypothesis and interpret the decision in the context of the original claim.**
\[ \text{Reject} \]
The null hypothesis. There **is** enough evidence to **support** the society's claim.
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