3) A newspaper publishes a study indicating that 45% of the population likes spicy food with a margin of error of ±7%.
A) What is the confidence interval? B)Would you conclude that most people like spicy food based on this interval?

Let's analyze the problem step by step.

### 3) A newspaper publishes a study indicating that 45% of the population likes spicy food with a margin of error of ±7%.

**A) What is the confidence interval?**

To find the confidence interval, we apply the margin of error to the sample proportion.

Given:
- Sample proportion \( p = 0.45 \)
- Margin of error \( \text{MOE} = 0.07 \)

The confidence interval is calculated as:

\[
\text{Confidence Interval} = p \pm \text{MOE} = 0.45 \pm 0.07
\]

This gives:

\[
\text{Confidence Interval} = (0.38, 0.52)
\]

So, the confidence interval is **38% to 52%**.

**B) Would you conclude that most people like spicy food based on this interval?**

To determine if most people (i.e., more than 50%) like spicy food, we need to see if the confidence interval lies above 50%.

- The lower bound of the interval is 38%, and the upper bound is 52%.
- Since the interval includes 50% and extends both below and slightly above it, we cannot conclusively say that most people like spicy food.

**Conclusion:** Based on this confidence interval, you cannot definitively conclude that most people like spicy food, as the interval overlaps with 50%.

Do you have any questions, or would you like further clarification?

### Related Questions:
1. How would increasing the margin of error to 10% affect the confidence interval?
2. What factors could lead to a large margin of error in a survey?
3. Why is it important to consider the confidence interval in public opinion polls?
4. How can increasing the sample size reduce the margin of error?
5. What are some possible sources of bias in survey results?

**Tip:** When interpreting confidence intervals, always check if the interval crosses a key threshold (like 50% in this case), as it impacts the strength of the conclusions you can draw.

Explore how confidence intervals are used to analyze public opinion polls with a focus on spicy food preferences. Learn about calculating confidence intervals and interpreting survey results. Suitable for advanced high school students and anyone interested in statistical analysis.

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