A survey asked, "How important is it to you to buy products that are made in America?" of the 600 Americans surveyed, 150 responded, "It is not important." For each of the following levels of confidence, find the sample proportion and the margin of error (MOE) associated with the poll. (Give the answers to one decimal place, if needed.)
(a) An 85% level of confidence
Sample proportion is

Incorrect: Your answer is incorrect.
%
MOE =
%

(b) A 98% level of confidence
Sample proportion is

Incorrect: Your answer is incorrect.
%
MOE =

Incorrect: Your answer is incorrect.

Let's go step by step to solve this problem for each confidence level.

### Step 1: Calculate the Sample Proportion (\( \hat{p} \))
The sample proportion is calculated by:

\[
\hat{p} = \frac{\text{Number of people who said "It is not important"}}{\text{Total number of surveyed people}}
\]

Here, we know:
- 150 people said "It is not important."
- The total sample size is 600.

So, the sample proportion is:

\[
\hat{p} = \frac{150}{600} = 0.25
\]

Thus, for both parts (a) and (b), the **sample proportion is 25%**.

### Step 2: Margin of Error Formula
The margin of error (MOE) is calculated using the formula:

\[
MOE = z^* \times \sqrt{\frac{\hat{p}(1 - \hat{p})}{n}}
\]

Where:
- \( z^* \) is the critical value corresponding to the given confidence level.
- \( \hat{p} \) is the sample proportion (0.25).
- \( n \) is the sample size (600).

Now, we need to calculate the MOE for each confidence level.

### (a) 85% Level of Confidence

For an 85% confidence level, the critical value \( z^* \) is approximately **1.44** (you can find this value from a standard normal distribution table).

Substitute the values into the MOE formula:

\[
MOE = 1.44 \times \sqrt{\frac{0.25 \times (1 - 0.25)}{600}}
= 1.44 \times \sqrt{\frac{0.25 \times 0.75}{600}}
= 1.44 \times \sqrt{\frac{0.1875}{600}}
= 1.44 \times \sqrt{0.0003125}
= 1.44 \times 0.01768
= 0.0255
\]

Thus, the margin of error is **0.0255**, or approximately **2.6%**.

### (b) 98% Level of Confidence

For a 98% confidence level, the critical value \( z^* \) is approximately **2.33**.

Substitute the values into the MOE formula:

\[
MOE = 2.33 \times \sqrt{\frac{0.25 \times (1 - 0.25)}{600}}
= 2.33 \times \sqrt{\frac{0.25 \times 0.75}{600}}
= 2.33 \times \sqrt{\frac{0.1875}{600}}
= 2.33 \times \sqrt{0.0003125}
= 2.33 \times 0.01768
= 0.0412
\]

Thus, the margin of error is **0.0412**, or approximately **4.1%**.

### Final Answers

(a) For an 85% confidence level:
- Sample proportion = **25%**
- MOE = **2.6%**

(b) For a 98% confidence level:
- Sample proportion = **25%**
- MOE = **4.1%**

---

Do you need any more details or explanations? Here are 5 follow-up questions to explore this topic further:

1. How does increasing the confidence level affect the margin of error?
2. What is the significance of the sample proportion in statistical analysis?
3. How would the margin of error change if the sample size were larger?
4. How is the critical value \( z^* \) determined for various confidence levels?
5. What are some potential sources of bias in surveys like the one described?

**Tip**: Confidence level and sample size are key factors affecting the margin of error in surveys. Larger sample sizes and lower confidence levels yield smaller margins of error.

A survey asked, 'How important is it to you to buy products that are made in America?' Of the 600 Americans surveyed, 150 responded, 'It is not important.' For each of the following levels of confidence, find the sample proportion and the margin of error (MOE) associated with the poll. (Give the answers to one decimal place, if needed.) (a) An 85% level of confidence Sample proportion is % MOE = % (b) A 98% level of confidence Sample proportion is % MOE = %

This solution explains how to calculate the sample proportion and margin of error (MOE) for confidence levels of 85% and 98% using survey data. The poll surveyed 600 Americans, with 150 responding that buying American-made products is 'not important.' Learn the statistical concepts of confidence intervals, sample proportion, and margin of error with detailed step-by-step calculations.

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