Consider the following table in reference to a hypothesis test: Ho True Ho false (1) (3) Accept Ho Reject Ho (2) (4) A Type Il error occurs when entry (1) is made. 1) True 2) False

MATLAB: An Introduction with Applications
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**Understanding Hypothesis Testing:**

Consider the following table in reference to a hypothesis test:

\[
\begin{array}{c|c|c}
& H_0 \text{ True} & H_0 \text{ False} \\
\hline
\text{Accept } H_0 & (1) & (2) \\
\text{Reject } H_0 & (3) & (4) \\
\end{array}
\]

The table is a framework used to understand the outcomes of hypothesis testing. 

- **Accept \(H_0\):** Refers to failing to reject the null hypothesis.
- **Reject \(H_0\):** Refers to rejecting the null hypothesis.

The numbers (1), (2), (3), and (4) represent possible outcomes:

- **(1):** True acceptance of \(H_0\) when it is true (correct decision).
- **(2):** Accepting \(H_0\) when it is false (Type II error).
- **(3):** Incorrectly rejecting \(H_0\) when it is true (Type I error).
- **(4):** Correctly rejecting \(H_0\) when it is false (correct decision).

**Question:**

A Type II error occurs when entry (1) is made.

- ⃝ 1) True
- ⃝ 2) False

**Answer Explanation:**

The statement is **False**. A Type II error occurs when you fail to reject the null hypothesis \(H_0\) when it is actually false, which corresponds to entry (2).
Transcribed Image Text:**Understanding Hypothesis Testing:** Consider the following table in reference to a hypothesis test: \[ \begin{array}{c|c|c} & H_0 \text{ True} & H_0 \text{ False} \\ \hline \text{Accept } H_0 & (1) & (2) \\ \text{Reject } H_0 & (3) & (4) \\ \end{array} \] The table is a framework used to understand the outcomes of hypothesis testing. - **Accept \(H_0\):** Refers to failing to reject the null hypothesis. - **Reject \(H_0\):** Refers to rejecting the null hypothesis. The numbers (1), (2), (3), and (4) represent possible outcomes: - **(1):** True acceptance of \(H_0\) when it is true (correct decision). - **(2):** Accepting \(H_0\) when it is false (Type II error). - **(3):** Incorrectly rejecting \(H_0\) when it is true (Type I error). - **(4):** Correctly rejecting \(H_0\) when it is false (correct decision). **Question:** A Type II error occurs when entry (1) is made. - ⃝ 1) True - ⃝ 2) False **Answer Explanation:** The statement is **False**. A Type II error occurs when you fail to reject the null hypothesis \(H_0\) when it is actually false, which corresponds to entry (2).
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