MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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According to a study, the proportion of people who are satisfied with the way things are going in their lives is 0.80. Suppose that a random sample of 100 people is obtained
According to a study, the proportion of people who are satisfied with the way things are going in their lives is 0.80. Suppose that a random sample of 100 people is obtained. Complete parts (a) through (c) below.

*Click here to view the standard normal distribution table (page 1).*
*Click here to view the standard normal distribution table (page 2).*

---

**(b) Explain why the sample proportion, p̂, is a random variable. What is the source of the variability?**

- **O A.** The sample proportion p̂ is a random variable because the value of p̂ represents a random person included in the sample. The variability is due to the fact that people may not be responding to the question truthfully.

- **O B.** The sample proportion p̂ is a random variable because the value of p̂ represents a random person included in the sample. The variability is due to the fact that different people feel differently regarding their satisfaction.

- **O C.** The sample proportion p̂ is a random variable because the value of p̂ varies from sample to sample. The variability is due to the fact that different people feel differently regarding their satisfaction.

- **O D.** The sample proportion p̂ is a random variable because the value of p̂ varies from sample to sample. The variability is due to the fact that people may not be responding to the question truthfully.

---

**(c) Describe the sampling distribution of p̂, the proportion of people who are satisfied with the way things are going in their life. Be sure to verify the model requirements.**

Since the sample size is no less than 5% of the population size and np(1 - p) ≥ 10, the distribution of p̂ is [normal distribution symbol] with μᵖ̂ = [0.80] and σᵖ̂ = [0.040].

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Transcribed Image Text:According to a study, the proportion of people who are satisfied with the way things are going in their lives is 0.80. Suppose that a random sample of 100 people is obtained. Complete parts (a) through (c) below. *Click here to view the standard normal distribution table (page 1).* *Click here to view the standard normal distribution table (page 2).* --- **(b) Explain why the sample proportion, p̂, is a random variable. What is the source of the variability?** - **O A.** The sample proportion p̂ is a random variable because the value of p̂ represents a random person included in the sample. The variability is due to the fact that people may not be responding to the question truthfully. - **O B.** The sample proportion p̂ is a random variable because the value of p̂ represents a random person included in the sample. The variability is due to the fact that different people feel differently regarding their satisfaction. - **O C.** The sample proportion p̂ is a random variable because the value of p̂ varies from sample to sample. The variability is due to the fact that different people feel differently regarding their satisfaction. - **O D.** The sample proportion p̂ is a random variable because the value of p̂ varies from sample to sample. The variability is due to the fact that people may not be responding to the question truthfully. --- **(c) Describe the sampling distribution of p̂, the proportion of people who are satisfied with the way things are going in their life. Be sure to verify the model requirements.** Since the sample size is no less than 5% of the population size and np(1 - p) ≥ 10, the distribution of p̂ is [normal distribution symbol] with μᵖ̂ = [0.80] and σᵖ̂ = [0.040]. [Next Button]
**Study on Satisfaction Rates**

According to a study, 80% (0.80) of people are satisfied with the way things are going in their lives. Suppose a random sample of 100 people is obtained.

**Tasks:**

- **View Standard Normal Distribution Tables:**
  - Page 1
  - Page 2

**Question (a):**  
If a random sample of 100 people is asked, "Are you satisfied with the way things are going in your life?" Is the response to this question qualitative or quantitative? Explain.

- **Options:**
  - **A.** The response is quantitative because the number of people satisfied can be counted.
  - **B.** The response is qualitative because the number of people satisfied can be counted.
  - **C.** The response is qualitative because the responses can be classified based on the characteristic of being satisfied or not.
  - **D.** The response is quantitative because the responses can be classified based on the characteristic of being satisfied or not.

**Question (b):**  
Explain why the sample proportion, \( \hat{p} \), is a random variable. What is the source of variability?

- **Options:**
  - **A.** The sample proportion \( \hat{p} \) is a random variable because the value of \( \hat{p} \) represents a random person included in the sample. The variability is due to the fact that people may not be responding to the question truthfully.
  - **B.** The sample proportion \( \hat{p} \) is a random variable because the value of \( \hat{p} \) represents a random person included in the sample. The variability is due to the fact that different people feel differently regarding their satisfaction.

**Instructions:**

- Review the options carefully.
- Consider the nature of qualitative versus quantitative data.
- Understand the concept of sample proportion as a random variable.
- Reflect on the sources of variability in survey responses.

Finally, select the most appropriate response before proceeding to the next step.
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Transcribed Image Text:**Study on Satisfaction Rates** According to a study, 80% (0.80) of people are satisfied with the way things are going in their lives. Suppose a random sample of 100 people is obtained. **Tasks:** - **View Standard Normal Distribution Tables:** - Page 1 - Page 2 **Question (a):** If a random sample of 100 people is asked, "Are you satisfied with the way things are going in your life?" Is the response to this question qualitative or quantitative? Explain. - **Options:** - **A.** The response is quantitative because the number of people satisfied can be counted. - **B.** The response is qualitative because the number of people satisfied can be counted. - **C.** The response is qualitative because the responses can be classified based on the characteristic of being satisfied or not. - **D.** The response is quantitative because the responses can be classified based on the characteristic of being satisfied or not. **Question (b):** Explain why the sample proportion, \( \hat{p} \), is a random variable. What is the source of variability? - **Options:** - **A.** The sample proportion \( \hat{p} \) is a random variable because the value of \( \hat{p} \) represents a random person included in the sample. The variability is due to the fact that people may not be responding to the question truthfully. - **B.** The sample proportion \( \hat{p} \) is a random variable because the value of \( \hat{p} \) represents a random person included in the sample. The variability is due to the fact that different people feel differently regarding their satisfaction. **Instructions:** - Review the options carefully. - Consider the nature of qualitative versus quantitative data. - Understand the concept of sample proportion as a random variable. - Reflect on the sources of variability in survey responses. Finally, select the most appropriate response before proceeding to the next step.
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