**Educational Transcription: Hypothesis Testing for Proportion Claims**A humane society claims that less than 63% of households in a certain country own a pet. In a random sample of 500 households in that country, 300 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.** More than ___ % of households in the country own a pet.- **B.** ___ % of households in the country own a pet.- **C.** Less than ___ % of households in the country own a pet.- **D.** The percentage of households in the country that own a pet is not ___ %.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 \leq $ ___- **B.** $ H_0 $: $ p \geq $ ___- **C.** $ H_0 $: $ p < $ ___- **D.** $ H_0 $: $ p > $ ___---**Explanation of Graphs or Diagrams:**In this text, there is no explicit graph or diagram. The information pertains purely to setting up a hypothesis test based on given data. The essential steps here involve determining the claim and then specifying the null hypothesis ($ H_0 $) and alternative hypothesis ($ H_a $) related to the proportion of households owning pets. The choices A, B, C, and D offer potential ways to frame the hypotheses, and the appropriate values need to be filled based on the claim (less than 63%) and the sample data provided. ### Hypothesis Testing on Pet Ownership in Households**Scenario:**A humane society asserts that less than 63% of households in a specified country have a pet. In a random sample of 500 households within that country, 300 households reported owning a pet. Given a significance level of $ \alpha = 0.10 $, you are tasked with determining if there is enough evidence to support the society's claim. **Instructions:**Complete parts (a) through (c) as outlined below:**(a) Define the Hypotheses:**Let $ p $ represent the population proportion of successes, where a success is defined as a household owning a pet. Establish the null hypothesis $ H_0 $ and alternative hypothesis $ H_a $. Select the appropriate hypothesis pair and fill in the corresponding values.(Round to two decimal places as necessary.)Options:A.\[ H_0: p \leq \_\_ \]\[ H_a: p > \_\_ \]B.\[ H_0: p \geq \_\_ \]\[ H_a: p < \_\_ \]C.\[ H_0: p < \_\_ \]\[ H_a: p \geq \_\_ \]D.\[ H_0: p \neq \_\_ \]\[ H_a: p = \_\_ \]E.\[ H_0: p > \_\_ \]\[ H_a: p \leq \_\_ \]F.\[ H_0: p = \_\_ \]\[ H_a: p \neq \_\_ \]**(b) P-Value Calculation:**Utilize statistical technology to compute the P-value for the test.**(c) Standardized Test Statistic:**Identify the standardized test statistic by calculating the z-score.\[ z = \_\_ \](Round to two decimal places as needed.)---**Explanation of Hypotheses:**When testing a hypothesis about a population proportion, we must set up our null and alternative hypotheses clearly:- The null hypothesis ($ H_0 $) usually represents the status quo or a statement of no effect or no difference.- The alternative hypothesis ($ H_a $) represents what we seek evidence for.Given the scenario, we assert that less than 63% of households own a pet. Therefore, our hypotheses are framed around this

A test is said to be normal if the population should be distributed normally and the value of sample…

A humane society claims that less than 63% of households in a certain country own a pet. In a random sample of 500 households in that country, 300 say they own a pet. At a = 0.10, 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.) O A. More than % of households in the country own a pet. OB. % of households in the country own a pet. O C. Less than % of households in the country own a pet. O D. The percentage households in the country that own a pet is not %. Let p be the population proportion of successes, where a success is a household in the country that owns a pet. State Ho and Ha. Select the correct choice below am fill in the answer boxes to complete your choice. (Round to two decimal places as needed.) O C. Ho: n<

A humane society claims that less than 63% of households in a certain country own a pet. In a random sample of 500 households in that country, 300 say they own a pet. At a = 0.10, 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.) O A. More than % of households in the country own a pet. OB. % of households in the country own a pet. O C. Less than % of households in the country own a pet. O D. The percentage households in the country that own a pet is not %. Let p be the population proportion of successes, where a success is a household in the country that owns a pet. State Ho and Ha. Select the correct choice below am fill in the answer boxes to complete your choice. (Round to two decimal places as needed.) O C. Ho: n<

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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Concept explainers

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.

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**Educational Transcription: Hypothesis Testing for Proportion Claims**

A humane society claims that less than 63% of households in a certain country own a pet. In a random sample of 500 households in that country, 300 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.** More than ___ % of households in the country own a pet.
- **B.** ___ % of households in the country own a pet.
- **C.** Less than ___ % of households in the country own a pet.
- **D.** The percentage of households in the country that own a pet is not ___ %.

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 \leq $ ___
- **B.** $ H_0 $: $ p \geq $ ___
- **C.** $ H_0 $: $ p < $ ___
- **D.** $ H_0 $: $ p > $ ___

---

**Explanation of Graphs or Diagrams:**

In this text, there is no explicit graph or diagram. The information pertains purely to setting up a hypothesis test based on given data. The essential steps here involve determining the claim and then specifying the null hypothesis ($ H_0 $) and alternative hypothesis ($ H_a $) related to the proportion of households owning pets. The choices A, B, C, and D offer potential ways to frame the hypotheses, and the appropriate values need to be filled based on the claim (less than 63%) and the sample data provided.

### Hypothesis Testing on Pet Ownership in Households

**Scenario:**

A humane society asserts that less than 63% of households in a specified country have a pet. In a random sample of 500 households within that country, 300 households reported owning a pet. Given a significance level of $ \alpha = 0.10 $, you are tasked with determining if there is enough evidence to support the society's claim.

**Instructions:**

Complete parts (a) through (c) as outlined below:

**(a) Define the Hypotheses:**

Let $ p $ represent the population proportion of successes, where a success is defined as a household owning a pet. Establish the null hypothesis $ H_0 $ and alternative hypothesis $ H_a $. Select the appropriate hypothesis pair and fill in the corresponding values.

(Round to two decimal places as necessary.)

Options:

A.
\[ H_0: p \leq \_\_ \]
\[ H_a: p > \_\_ \]

B.
\[ H_0: p \geq \_\_ \]
\[ H_a: p < \_\_ \]

C.
\[ H_0: p < \_\_ \]
\[ H_a: p \geq \_\_ \]

D.
\[ H_0: p \neq \_\_ \]
\[ H_a: p = \_\_ \]

E.
\[ H_0: p > \_\_ \]
\[ H_a: p \leq \_\_ \]

F.
\[ H_0: p = \_\_ \]
\[ H_a: p \neq \_\_ \]

**(b) P-Value Calculation:**

Utilize statistical technology to compute the P-value for the test.

**(c) Standardized Test Statistic:**

Identify the standardized test statistic by calculating the z-score.

\[ z = \_\_ \]

(Round to two decimal places as needed.)

---

**Explanation of Hypotheses:**

When testing a hypothesis about a population proportion, we must set up our null and alternative hypotheses clearly:

- The null hypothesis ($ H_0 $) usually represents the status quo or a statement of no effect or no difference.
- The alternative hypothesis ($ H_a $) represents what we seek evidence for.

Given the scenario, we assert that less than 63% of households own a pet. Therefore, our hypotheses are framed around this

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