MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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Transcribed Image Text:### Hypothesis Testing and Error Types
**Scenario:**
Three years ago, the mean price of an existing single-family home was $243,761. A real estate broker believes that existing home prices in her neighborhood are lower.
**Tasks:**
**(a) State the null and alternative hypotheses in words.**
**(b) State the null and alternative hypotheses symbolically.**
**(c) Explain what it would mean to make a Type I error.**
**(d) Explain what it would mean to make a Type II error.**
---
**(a) State the null hypothesis in words. Choose the correct answer below.**
- **A.** The mean price of a single-family home in the broker's neighborhood is $243,761.
- **B.** The mean price of a single-family home in the broker's neighborhood is different from $243,761.
- **C.** The mean price of a single-family home in the broker's neighborhood is less than $243,761.
- **D.** The mean price of a single-family home in any neighborhood is $243,761.
**Answer: A**
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Follow-up Question
![(c) What would it mean to make a Type I error?
The broker **rejects** the hypothesis that the mean price is **equal to** \($243,761\), when the true mean price is **equal to** \($243,761\).
(Type integers or decimals. Do not round.)
(d) What would it mean to make a Type II error?
The broker \[dropdown menu\] the hypothesis that the mean price is \[dropdown menu\] \($[\text{input box}]\), when the true mean price is \($[\text{input box}]\).
(Type integers or decimals. Do not round.)](https://content.bartleby.com/qna-images/question/ac3be618-b645-4bd8-855b-808ff3fc18d4/817d16c0-abdf-4e06-979b-1755c837a750/ngfcu6l_processed.jpeg)
Transcribed Image Text:(c) What would it mean to make a Type I error?
The broker **rejects** the hypothesis that the mean price is **equal to** \($243,761\), when the true mean price is **equal to** \($243,761\).
(Type integers or decimals. Do not round.)
(d) What would it mean to make a Type II error?
The broker \[dropdown menu\] the hypothesis that the mean price is \[dropdown menu\] \($[\text{input box}]\), when the true mean price is \($[\text{input box}]\).
(Type integers or decimals. Do not round.)
Solution
by Bartleby Expert
Follow-up Question
![### Hypothesis Testing Process
**(b) State the hypotheses clearly:**
- \( H_0: \mu \)
- \( H_1: \mu \)
(Type integers or decimals. Do not round.)
**(c) What would result in a Type I error?**
The broker [drop-down menu: "rejects"/"fails to reject"] the hypothesis that the mean price is \( \_\_ \) \$ when the true mean price is [drop-down menu: "rejects"/"fails to reject"] \( \_\_ \) \$.
(Type integers or decimals. Do not round.)](https://content.bartleby.com/qna-images/question/ac3be618-b645-4bd8-855b-808ff3fc18d4/9c5a97a2-03dc-436d-807d-a679c6d6d87c/pcrwiu_processed.jpeg)
Transcribed Image Text:### Hypothesis Testing Process
**(b) State the hypotheses clearly:**
- \( H_0: \mu \)
- \( H_1: \mu \)
(Type integers or decimals. Do not round.)
**(c) What would result in a Type I error?**
The broker [drop-down menu: "rejects"/"fails to reject"] the hypothesis that the mean price is \( \_\_ \) \$ when the true mean price is [drop-down menu: "rejects"/"fails to reject"] \( \_\_ \) \$.
(Type integers or decimals. Do not round.)
Solution
by Bartleby Expert
Follow-up Question
Transcribed Image Text:**Understanding Hypothesis Testing in Real Estate Pricing**
Three years ago, the mean price of an existing single-family home was $243,761. A real estate broker believes that existing home prices in her neighborhood are lower. To assess this claim, we will explore hypothesis testing.
**(a) State the Null Hypothesis in Words:**
The null hypothesis (H0) is a statement that there is no effect or no difference. For this scenario, the null hypothesis is:
- A. The mean price of a single-family home in the broker's neighborhood is $243,761.
**(b) State the Alternative Hypothesis in Words:**
The alternative hypothesis (H1) is what we seek evidence for, suggesting there is an effect or a difference. In this case, the alternative hypothesis is:
- C. The mean price of a single-family home in the broker's neighborhood is less than $243,761.
**Understanding Errors in Hypothesis Testing:**
**(c) Type I Error:**
A Type I error occurs when the null hypothesis is true, but we incorrectly reject it. In this context, a Type I error would mean concluding that the mean price is less than $243,761 when it is actually $243,761.
**(d) Type II Error:**
A Type II error happens when the null hypothesis is false, but we fail to reject it. Here, it would mean failing to conclude that the mean price is less than $243,761 when it is actually lower.
This process of hypothesis testing assists in making informed decisions based on data.
Solution
by Bartleby Expert
Follow-up Questions
Read through expert solutions to related follow-up questions below.
Follow-up Question
Transcribed Image Text:(c) What would it mean to make a Type I error?
The broker **rejects** the hypothesis that the mean price is **equal to** \($243,761\), when the true mean price is **equal to** \($243,761\).
(Type integers or decimals. Do not round.)
(d) What would it mean to make a Type II error?
The broker \[dropdown menu\] the hypothesis that the mean price is \[dropdown menu\] \($[\text{input box}]\), when the true mean price is \($[\text{input box}]\).
(Type integers or decimals. Do not round.)
Solution
by Bartleby Expert
Follow-up Question
Transcribed Image Text:### Hypothesis Testing Process
**(b) State the hypotheses clearly:**
- \( H_0: \mu \)
- \( H_1: \mu \)
(Type integers or decimals. Do not round.)
**(c) What would result in a Type I error?**
The broker [drop-down menu: "rejects"/"fails to reject"] the hypothesis that the mean price is \( \_\_ \) \$ when the true mean price is [drop-down menu: "rejects"/"fails to reject"] \( \_\_ \) \$.
(Type integers or decimals. Do not round.)
Solution
by Bartleby Expert
Follow-up Question
Transcribed Image Text:**Understanding Hypothesis Testing in Real Estate Pricing**
Three years ago, the mean price of an existing single-family home was $243,761. A real estate broker believes that existing home prices in her neighborhood are lower. To assess this claim, we will explore hypothesis testing.
**(a) State the Null Hypothesis in Words:**
The null hypothesis (H0) is a statement that there is no effect or no difference. For this scenario, the null hypothesis is:
- A. The mean price of a single-family home in the broker's neighborhood is $243,761.
**(b) State the Alternative Hypothesis in Words:**
The alternative hypothesis (H1) is what we seek evidence for, suggesting there is an effect or a difference. In this case, the alternative hypothesis is:
- C. The mean price of a single-family home in the broker's neighborhood is less than $243,761.
**Understanding Errors in Hypothesis Testing:**
**(c) Type I Error:**
A Type I error occurs when the null hypothesis is true, but we incorrectly reject it. In this context, a Type I error would mean concluding that the mean price is less than $243,761 when it is actually $243,761.
**(d) Type II Error:**
A Type II error happens when the null hypothesis is false, but we fail to reject it. Here, it would mean failing to conclude that the mean price is less than $243,761 when it is actually lower.
This process of hypothesis testing assists in making informed decisions based on data.
Solution
by Bartleby Expert
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