## Problem Description: First Generation College Students

**Question Set 1_A: Research Question**: Do more than 25% of all World Campus students identify as first-generation students?

**Steps:**

**Figure 0.1: Randomization test for a proportion
**

**1. Hypotheses:
**

- Null Hypothesis: 0.25H0:P≤0.25
- Alternative Hypothesis: 0.25HA:P>0.25

**2. Randomization Distribution:
**

- Use StatKey to construct a randomization distribution with at least 5000 resamples.

**3. P-Value Calculation:
**

- According to StatKey, the p-value is 0.935 in a right-tailed test.

**Figure 2: Using StatKey to construct a randomization distribution
**

4. Decision:

- Since the p-value > significance level, fails to reject the null hypothesis.

5. Conclusion:

- We lack sufficient evidence to support the claim that more than 25% of all World Campus students identify as first-generation students.

## Question Set 1_C:

- Compare results from parts 1_A and 1_B.
- Explain why the p-value changed with the increase in sample size.
- The p-value changed due to the larger sample size providing more precise estimates of the population proportion, resulting in a narrower distribution around the hypothesized proportion.

**Problem Description: Credit Card Fraud Detection
**

**Question Set 2_A: Research Question**: Does the new AI technology detect fraudulent charges more than 97% of the time?

**Hypotheses:
**

**Null Hypothesis**: 0.97H0:P≤0.97**Alternative Hypothesis**: 0.97HA:P>0.97

**Question Set 2_B: Type I Error**:

- Falsely rejects the null hypothesis, indicating the technology detects fraud more than 97% when it does not.
- Consequence: Wasting resources and implementing an ineffective system.

**Question Set 2_C: Type II Error**:

- Fails to reject the null hypothesis, suggesting the technology does not detect fraud more than 97% when it does.
- Consequence: Missing the chance to enhance fraud detection and exposing customers to fraudulent activity.

**Question Set 2_D: Severity Comparison:
**

- In this scenario, a Type II error is more serious. Failing to invest in the new technology could lead to continued losses from fraudulent charges and potential harm to customers.

**Question Set 2_E: Alpha Level Choice:
**

- Given the consequences, a lower alpha level (e.g., 0.05) is recommended to reduce the likelihood of Type II error.

**Reflection:
**

**Confidence Level:**- High confidence in answers grounded in provided information and hypothesis testing principles.
**Challenges:**- Determining the severity of errors in the specific context was the most challenging aspect.