The data given to the right includes data from 40 candies, and 5 of them are red. The company that makes the candy claims that 33% of its candies are red. Use the sample data to construct a 95% confidence interval estimate of the percentage of red candies. What do you conclude about the claim of 33%? Construct a 95% confidence interval estimate of the population percentage of candies that are red. %

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The image contains statistical data and instructions for constructing a 95% confidence interval. Here's a detailed transcription as might appear on an educational website:

---

### Constructing a 95% Confidence Interval for Candy Color Distribution

**Context:**
The data includes information from a sample of 40 candies, out of which 5 are red. The candy company claims that 33% of its candies are red. The challenge is to use the sample data to construct a 95% confidence interval and verify the company's claim regarding the percentage of red candies.

**Task:**
Construct a 95% confidence interval estimate of the population percentage of candies that are red.

**Calculation:**
- \( \_\_\_\_ \% < p < \_\_\_\_ \% \)
- (Type an integer or decimal rounded to one decimal place as needed.)

**Evaluation:**
"Is the result consistent with the 33% rate that is reported by the candy maker?"

- Options:
  - Yes, because the confidence interval includes 33%.
  - No, because the confidence interval does not include 33%.

---

**Additional Data:**
The table on the right provides the weights (in grams) of a sample bag of candy, categorized by color:

- **Red:** 
  - 0.934, 0.993, 0.749, 0.882, 0.991
- **Blue:** 
  - 0.759, 0.712, 0.833, 0.709, 0.894
- **Brown:** 
  - 0.935, 0.899, 0.718, 0.941, 0.867
- **Green:** 
  - 0.957, 0.979, 0.987, 0.926, 0.827
- **Yellow:** 
  - 0.723, 0.709, 0.749, 0.745, 0.905, 0.979, 0.817, 0.987

**Graph/Diagram Explanation:**
The table serves as supporting data for evaluating the proportion of red candies and other colors by showcasing the variation in their weights.

---
Transcribed Image Text:The image contains statistical data and instructions for constructing a 95% confidence interval. Here's a detailed transcription as might appear on an educational website: --- ### Constructing a 95% Confidence Interval for Candy Color Distribution **Context:** The data includes information from a sample of 40 candies, out of which 5 are red. The candy company claims that 33% of its candies are red. The challenge is to use the sample data to construct a 95% confidence interval and verify the company's claim regarding the percentage of red candies. **Task:** Construct a 95% confidence interval estimate of the population percentage of candies that are red. **Calculation:** - \( \_\_\_\_ \% < p < \_\_\_\_ \% \) - (Type an integer or decimal rounded to one decimal place as needed.) **Evaluation:** "Is the result consistent with the 33% rate that is reported by the candy maker?" - Options: - Yes, because the confidence interval includes 33%. - No, because the confidence interval does not include 33%. --- **Additional Data:** The table on the right provides the weights (in grams) of a sample bag of candy, categorized by color: - **Red:** - 0.934, 0.993, 0.749, 0.882, 0.991 - **Blue:** - 0.759, 0.712, 0.833, 0.709, 0.894 - **Brown:** - 0.935, 0.899, 0.718, 0.941, 0.867 - **Green:** - 0.957, 0.979, 0.987, 0.926, 0.827 - **Yellow:** - 0.723, 0.709, 0.749, 0.745, 0.905, 0.979, 0.817, 0.987 **Graph/Diagram Explanation:** The table serves as supporting data for evaluating the proportion of red candies and other colors by showcasing the variation in their weights. ---
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