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claim and hypothesis for the PROPORTION. 1. what claim about a proportion from the article did we test 2. what was our null hypothesis for the proportion 3. what was the alternative hypothesis

It looks like you uploaded an image that relates to a student solution worksheet involving statistics and hypothesis testing, specifically focusing on proportions. To address your question:

### 1. **What claim about a proportion did we test?**
   The claim you are referring to is likely a statement regarding the population proportion of a particular group or category. Based on the content from your image (related to descriptive statistics), you might have tested the claim that a certain proportion of the population (perhaps age or gender) falls within a specific category. For example, the proportion of males or females in a certain age group.

   An example of a claim could be:
   - "The proportion of students over 30 years old is greater than 0.25."

### 2. **What was our null hypothesis for the proportion?**
   The null hypothesis (\( H_0 \)) for the proportion would typically state that the proportion is equal to a specified value. If the claim is that the proportion is greater than a certain value, the null hypothesis would be the opposite.

   For example, if you are testing whether the proportion of students over 30 is greater than 0.25, the null hypothesis would be:
   - \( H_0: p = 0.25 \)
   
   This indicates that the proportion of students over 30 is equal to 25%.

### 3. **What was the alternative hypothesis?**
   The alternative hypothesis (\( H_1 \)) would be the opposite of the null hypothesis and would represent the claim you are testing.

   Continuing with the same example, if you are claiming that the proportion is greater than 0.25, the alternative hypothesis would be:
   - \( H_1: p > 0.25 \)
   
   This indicates that the proportion of students over 30 is greater than 25%.

Would you like me to clarify the context further based on the image content, or provide detailed steps on how to test a hypothesis for proportions?

### 5 Related Questions:
1. How do you calculate the sample proportion (\( \hat{p} \)) for a proportion test?
2. What is the difference between a one-tailed and two-tailed hypothesis test?
3. How do you determine the critical value for a hypothesis test on proportions?
4. What is the p-value in the context of hypothesis testing for proportions, and how do you interpret it?
5. What conditions must be met to perform a hypothesis test on a proportion?

### Tip:
When performing a hypothesis test for proportions, always ensure the sample size is large enough to satisfy the condition: \( n \times p \geq 10 \) and \( n \times (1 - p) \geq 10 \) for valid approximations using the normal distribution.

Understand how to conduct a hypothesis test for a proportion with this detailed explanation. Learn how to identify the claim, null hypothesis (H0), and alternative hypothesis (H1) based on a given proportion claim, using key statistical concepts. Suitable for college-level statistics students.

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