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Let's walk through the problem shown in the image, which is a hypothesis test for proportions.

### Problem Summary:
- The claim is that the percentage of children aged 8-12 who have phones differs from 52%.
- A survey shows that 449 out of 832 children have phones.
- We are asked to test this claim at a significance level of \( \alpha = 0.10 \) using the P-value method.

### Step 1: Stating the Hypotheses
We are testing whether the percentage (proportion) of children who have phones differs from 52%. This is a two-tailed hypothesis test since the wording says "differs from" rather than something directional like "greater than" or "less than."

- **Null hypothesis (\(H_0\))**: The proportion of children who have phones is 52%, or \( p = 0.52 \).
  
- **Alternative hypothesis (\(H_1\))**: The proportion of children who have phones is not 52%, or \( p \neq 0.52 \).

### Step 2: Determine the Type of Test
Since we're dealing with proportions, this will be a **proportion z-test**.

Would you like to proceed with the remaining steps of the hypothesis test, such as calculating the test statistic and P-value? If yes, I can help guide you through those steps as well.

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Here are 5 related questions to expand your understanding:
1. How do you calculate the test statistic in a z-test for proportions?
2. What is the P-value, and how does it help in hypothesis testing?
3. Why is this test considered a two-tailed test?
4. How would the test change if the alternative hypothesis stated that the proportion is greater than 52%?
5. How do you interpret the results of a hypothesis test if the P-value is smaller than the significance level?

### Tip:
Always check whether your test is one-tailed or two-tailed based on the wording of the claim—phrases like "differs" indicate a two-tailed test!

A marketing manager for a phone company claims that the percentage of children aged 8-12 who have phones differs from 52%. In a survey of 832 children aged 8-12, 449 of them had phones. Can you conclude that the manager's claim is true? Use the α = 0.10 level of significance and the P-value method with the TI-84 Plus calculator.

Learn how to conduct a hypothesis test for proportions using a sample of 832 children aged 8-12, where 449 had phones. Test the claim that the proportion differs from 52% at a significance level of α = 0.10 using the P-value method. Suitable for statistics students in Grades 11-12.

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