### 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**

a)It is needed to define the null and alternative hypotheses.

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. (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 Il error. (a) State the null hypothesis in words. Choose the correct answer below. O A. The mean price of a single family home in the broker's neighborhood is $243,761 OB. The mean price of a single family home in the broker's neighborhood is different from $243,761. OC. The mean price of a single family home in the broker's neighborhood is less than $243,761. O D. The mean price of a single family home in any neighborhood is $243.761

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. (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 Il error. (a) State the null hypothesis in words. Choose the correct answer below. O A. The mean price of a single family home in the broker's neighborhood is $243,761 OB. The mean price of a single family home in the broker's neighborhood is different from $243,761. OC. The mean price of a single family home in the broker's neighborhood is less than $243,761. O D. The mean price of a single family home in any neighborhood is $243.761

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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Question

### 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 Questions

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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.)

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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.)

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Follow-up Question

**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.

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