According to the February 2008 Federal Trade Commission report on consumer fraud and identity theft, 23% of all complaints in 2007 were for identity theft. In that year, assume some state had 436 complaints of identity theft out of 1680 consumer complaints. Do these data provide enough evidence to show that that state had a higher proportion of identity theft than 23%? Test at the 4% level.

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please do the following parts, this is one question!

hypotheses, assumptions, and please check the assumptions (listed as a problem in the image)

### Understanding Hypothesis Testing for Consumer Fraud and Identity Theft

**Context:**

According to the February 2008 Federal Trade Commission report on consumer fraud and identity theft, 23% of all complaints in 2007 were for identity theft. In that year, a certain state reported 436 identity theft complaints out of 1680 consumer complaints. We aim to determine if this state had a higher proportion of identity theft complaints than 23% at a 4% significance level.

---

**P: Parameter**

- **Question:** What is the correct parameter symbol for this problem?

- **Answer:** \( p \)

- **Contextual Definition:** The percentage of all consumer complaints in that state that are for identity theft.

---

**H: Hypotheses**

- **Null Hypothesis (\( H_0 \)):** \( p = 0.23 \)

- **Alternative Hypothesis (\( H_A \)):** \( p > 0.23 \)

---

**A: Assumptions**

- Since **qualitative** information was collected from each object, we need to check the following conditions:

  - \( \sigma \) is unknown.
  
  - \( np \ge 10 \)
  
  - \( nq = n(1-p) \ge 10 \)

- **Calculations:**

  - \( np \): Calculate and verify if this value is \( \ge 10 \). Consider the formula: 
    - \( np = 1680 \times 0.23 \)

  - \( n(1-p) \): Calculate and verify if this value is \( \ge 10 \). Use the formula:
    - \( n(1-p) = 1680 \times (1-0.23) \)

  - **Sample Size (N):** Verify the total sample size:
    - Given \( N = 1680 \)

---

**N: Name the Procedure**

- Based on the calculations and conditions met, select an appropriate hypothesis test. Options are likely to include:

  - One-Proportion Z-Test

---

This exercise involves understanding the assumptions and conditions necessary for performing a hypothesis test on proportions and applying this to determine if a specific state's proportion of identity theft complaints significantly differs from the national average.
Transcribed Image Text:### Understanding Hypothesis Testing for Consumer Fraud and Identity Theft **Context:** According to the February 2008 Federal Trade Commission report on consumer fraud and identity theft, 23% of all complaints in 2007 were for identity theft. In that year, a certain state reported 436 identity theft complaints out of 1680 consumer complaints. We aim to determine if this state had a higher proportion of identity theft complaints than 23% at a 4% significance level. --- **P: Parameter** - **Question:** What is the correct parameter symbol for this problem? - **Answer:** \( p \) - **Contextual Definition:** The percentage of all consumer complaints in that state that are for identity theft. --- **H: Hypotheses** - **Null Hypothesis (\( H_0 \)):** \( p = 0.23 \) - **Alternative Hypothesis (\( H_A \)):** \( p > 0.23 \) --- **A: Assumptions** - Since **qualitative** information was collected from each object, we need to check the following conditions: - \( \sigma \) is unknown. - \( np \ge 10 \) - \( nq = n(1-p) \ge 10 \) - **Calculations:** - \( np \): Calculate and verify if this value is \( \ge 10 \). Consider the formula: - \( np = 1680 \times 0.23 \) - \( n(1-p) \): Calculate and verify if this value is \( \ge 10 \). Use the formula: - \( n(1-p) = 1680 \times (1-0.23) \) - **Sample Size (N):** Verify the total sample size: - Given \( N = 1680 \) --- **N: Name the Procedure** - Based on the calculations and conditions met, select an appropriate hypothesis test. Options are likely to include: - One-Proportion Z-Test --- This exercise involves understanding the assumptions and conditions necessary for performing a hypothesis test on proportions and applying this to determine if a specific state's proportion of identity theft complaints significantly differs from the national average.
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