MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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### Understanding Confidence Intervals and Hypothesis Testing

**Concept:**
The three confidence intervals shown below represent three samplings. The objective is to decide whether each confidence interval indicates that you should reject the null hypothesis \( H_0 \). The null hypothesis in this case is \( H_0: p \leq 0.24 \).

### Graphs Explanation:

1. **Hypothesis Range Representation:**
   - A horizontal bar indicates the value range where \( p \leq 0.24 \) (up to 0.24 on the scale).

2. **Confidence Interval Graphs:**
   - **Interval (a):** The confidence interval (CI) ranges from \( 0.25 < p < 0.26 \).
   - **Interval (b):** The confidence interval (CI) ranges from \( 0.21 < p < 0.23 \).
   - **Interval (c):** The confidence interval (CI) ranges from \( 0.225 < p < 0.265 \).

### Questions and Answers:

#### (a) Choose the correct answer below:

- **A. Fail to reject \( H_0 \). The confidence interval includes values less than 0.24.**
- **B. Reject \( H_0 \). The confidence interval is located to the right of 0.24.**
- **C. Reject \( H_0 \). The confidence interval includes values less than 0.24.**
- **D. Fail to reject \( H_0 \). The confidence interval is located to the right of 0.24.**

#### (b) Choose the correct answer below:

- **A. Fail to reject \( H_0 \). The confidence interval includes values greater than 0.24.**
- **B. Fail to reject \( H_0 \). The confidence interval includes values less than 0.24.**
- **C. Reject \( H_0 \). The confidence interval includes values greater than 0.24.**
- **D. Reject \( H_0 \). The confidence interval includes values less than 0.24.**

### Explanation:

1. **Decision for Interval (a):**
   - The interval \( 0.25 < p < 0.26 \) lies entirely to the right of 0.24.
   - You should **reject \( H_0 \)** because the
Transcribed Image Text:### Understanding Confidence Intervals and Hypothesis Testing **Concept:** The three confidence intervals shown below represent three samplings. The objective is to decide whether each confidence interval indicates that you should reject the null hypothesis \( H_0 \). The null hypothesis in this case is \( H_0: p \leq 0.24 \). ### Graphs Explanation: 1. **Hypothesis Range Representation:** - A horizontal bar indicates the value range where \( p \leq 0.24 \) (up to 0.24 on the scale). 2. **Confidence Interval Graphs:** - **Interval (a):** The confidence interval (CI) ranges from \( 0.25 < p < 0.26 \). - **Interval (b):** The confidence interval (CI) ranges from \( 0.21 < p < 0.23 \). - **Interval (c):** The confidence interval (CI) ranges from \( 0.225 < p < 0.265 \). ### Questions and Answers: #### (a) Choose the correct answer below: - **A. Fail to reject \( H_0 \). The confidence interval includes values less than 0.24.** - **B. Reject \( H_0 \). The confidence interval is located to the right of 0.24.** - **C. Reject \( H_0 \). The confidence interval includes values less than 0.24.** - **D. Fail to reject \( H_0 \). The confidence interval is located to the right of 0.24.** #### (b) Choose the correct answer below: - **A. Fail to reject \( H_0 \). The confidence interval includes values greater than 0.24.** - **B. Fail to reject \( H_0 \). The confidence interval includes values less than 0.24.** - **C. Reject \( H_0 \). The confidence interval includes values greater than 0.24.** - **D. Reject \( H_0 \). The confidence interval includes values less than 0.24.** ### Explanation: 1. **Decision for Interval (a):** - The interval \( 0.25 < p < 0.26 \) lies entirely to the right of 0.24. - You should **reject \( H_0 \)** because the
## Understanding Confidence Intervals and Hypothesis Testing

The three confidence intervals displayed represent three distinct samplings. Your task is to determine whether each confidence interval suggests rejecting the null hypothesis \(H_0\). Please justify your reasoning.

### Hypothesis
\(H_0\): \(p \leq 0.24\)

### Graphical Representation

There are three intervals labeled (a), (b), and (c):
- **Interval (a)**: \(0.25 < p < 0.26\)
- **Interval (b)**: \(0.21 < p < 0.23\)
- **Interval (c)**: \(0.225 < p < 0.265\)

The intervals are marked on a continuous scale from 0.21 to 0.27.

**Choice Section**

#### (b) Choose the correct answer below for Interval (a):

- \( \circ \) **A.** Fail to reject \(H_0\). The confidence interval includes values greater than 0.24.
- \( \circ \) **B.** Fail to reject \(H_0\). The confidence interval includes values less than 0.24.
- \( \circ \) **C.** Reject \(H_0\). The confidence interval includes values greater than 0.24.
- \( \circ \) **D.** Reject \(H_0\). The confidence interval includes values less than 0.24.

#### (c) Choose the correct answer below for Intervals (b) & (c):

- \( \circ \) **A.** Reject \(H_0\). The confidence interval includes values less than 0.24.
- \( \circ \) **B.** Fail to reject \(H_0\). The confidence interval includes values less than 0.24.
- \( \circ \) **C.** Fail to reject \(H_0\). The confidence interval includes values greater than 0.24.
- \( \circ \) **D.** Reject \(H_0\). The confidence interval includes values greater than 0.24.

### Explanation

To determine whether to reject or fail to reject \(H_0\), observe where the intervals lie in relation to the null hypothesis boundary \(p = 0.24\):

1. **Interval (a)**: \(0.25 < p < 0.
Transcribed Image Text:## Understanding Confidence Intervals and Hypothesis Testing The three confidence intervals displayed represent three distinct samplings. Your task is to determine whether each confidence interval suggests rejecting the null hypothesis \(H_0\). Please justify your reasoning. ### Hypothesis \(H_0\): \(p \leq 0.24\) ### Graphical Representation There are three intervals labeled (a), (b), and (c): - **Interval (a)**: \(0.25 < p < 0.26\) - **Interval (b)**: \(0.21 < p < 0.23\) - **Interval (c)**: \(0.225 < p < 0.265\) The intervals are marked on a continuous scale from 0.21 to 0.27. **Choice Section** #### (b) Choose the correct answer below for Interval (a): - \( \circ \) **A.** Fail to reject \(H_0\). The confidence interval includes values greater than 0.24. - \( \circ \) **B.** Fail to reject \(H_0\). The confidence interval includes values less than 0.24. - \( \circ \) **C.** Reject \(H_0\). The confidence interval includes values greater than 0.24. - \( \circ \) **D.** Reject \(H_0\). The confidence interval includes values less than 0.24. #### (c) Choose the correct answer below for Intervals (b) & (c): - \( \circ \) **A.** Reject \(H_0\). The confidence interval includes values less than 0.24. - \( \circ \) **B.** Fail to reject \(H_0\). The confidence interval includes values less than 0.24. - \( \circ \) **C.** Fail to reject \(H_0\). The confidence interval includes values greater than 0.24. - \( \circ \) **D.** Reject \(H_0\). The confidence interval includes values greater than 0.24. ### Explanation To determine whether to reject or fail to reject \(H_0\), observe where the intervals lie in relation to the null hypothesis boundary \(p = 0.24\): 1. **Interval (a)**: \(0.25 < p < 0.
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