A survey of 1000 adults in the US conducted in March 2011 asked "Do you favor or oppose 'sin taxes' on soda and junk food?" The proportion in favor of taxing these foods was 32 %.1 "32% favor 'sin taxes' on soda, junk food", Rasmussen Reports, April 1, 2011. (a) Find a 90% confidence interval for the proportion of US adults favoring taxes on soda and junk food. Round your answers to three decimal places. The 90% confidence interval is to

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### Public Opinion on 'Sin Taxes' on Soda and Junk Food

A survey conducted in March 2011 questioned 1000 adults in the US about their stance on 'sin taxes' on soda and junk food. The survey specifically asked, "Do you favor or oppose 'sin taxes' on soda and junk food?" The findings revealed that 32% of the respondents were in favor of taxing these types of foods. 

> "32% favor ‘sin taxes’ on soda, junk food”, Rasmussen Reports, April 1, 2011.

### Statistical Analysis

**(a) 90% Confidence Interval Calculation:**
To determine the confidence interval for the proportion of US adults who favor taxes on soda and junk food, follow these steps:

1. **Identify the sample proportion (p):**
   - Proportion (p) = 0.32

2. **Determine the standard error (SE) using the formula:**
   - SE = sqrt [ p(1 - p) / n ]
   - Where n is the sample size (1000 adults)

3. **Calculate the margin of error (ME) for a 90% confidence level:**
   - For a 90% confidence level, the z-value (z*) is approximately 1.645.
   - ME = z* * SE

4. **Construct the confidence interval:**
   - Lower limit = p - ME
   - Upper limit = p + ME

**Compute the confidence interval and round the results to three decimal places:**
The 90% confidence interval is \(\_\_\_\) to \(\_\_\_\).
Transcribed Image Text:### Public Opinion on 'Sin Taxes' on Soda and Junk Food A survey conducted in March 2011 questioned 1000 adults in the US about their stance on 'sin taxes' on soda and junk food. The survey specifically asked, "Do you favor or oppose 'sin taxes' on soda and junk food?" The findings revealed that 32% of the respondents were in favor of taxing these types of foods. > "32% favor ‘sin taxes’ on soda, junk food”, Rasmussen Reports, April 1, 2011. ### Statistical Analysis **(a) 90% Confidence Interval Calculation:** To determine the confidence interval for the proportion of US adults who favor taxes on soda and junk food, follow these steps: 1. **Identify the sample proportion (p):** - Proportion (p) = 0.32 2. **Determine the standard error (SE) using the formula:** - SE = sqrt [ p(1 - p) / n ] - Where n is the sample size (1000 adults) 3. **Calculate the margin of error (ME) for a 90% confidence level:** - For a 90% confidence level, the z-value (z*) is approximately 1.645. - ME = z* * SE 4. **Construct the confidence interval:** - Lower limit = p - ME - Upper limit = p + ME **Compute the confidence interval and round the results to three decimal places:** The 90% confidence interval is \(\_\_\_\) to \(\_\_\_\).
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