A CBS News/New York Times poll found the 30 out of 990 Americans said they think the most important problem facing the U.S. is health care. Estimate the true proportion with a 96% confidence of Americans who think that this is the most important problem. Margin of error: Interval Calculation E = 0.0112 0.0303 0.0112 < p < 0.0303 +0.0112 0.0191 < p < 0.0415 1.91% < p < 4.15% Write the confidence statement in the box below: Distribution Statistics Z Estimate of a Proportion Confidence Level 0.96 Successes 30 N 990 Result Sample Z Estimate of a Proportion

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### Analysis of Poll Results on Healthcare as the Most Important Issue

A CBS News/New York Times poll surveyed 990 Americans to determine their views on the most important problem facing the U.S. health care system. Out of those surveyed, 30 respondents identified health care as the top issue. We can estimate the true proportion of Americans holding this view using a 96% confidence interval.

#### Margin of Error
- **E** = 0.0112

#### Interval Calculation
To calculate the confidence interval, we adjust the observed proportion by the margin of error.

- Calculated Interval: 
  \[
  0.0303 - 0.0112 < p < 0.0303 + 0.0112
  \]
  \[
  0.0191 < p < 0.0415
  \]

Expressed in percentage, the interval is:
- **1.91% < p < 4.15%**

This interval estimates that between 1.91% and 4.15% of Americans believe health care is the most important problem.

#### Graph Explanation
A table is provided to support the calculations:
- **Z Estimate of a Proportion**:
  - **Successes**: 30
  - **Sample Size (N)**: 990
  - **Standard Error (SE)**: 0.0054
  - **Lower Limit**: 0.0191
  - **Upper Limit**: 0.0415
  - **Interval**: 0.0303 ± 0.0112

The results are visually supported with a structured data table to ensure clarity in understanding the confidence interval calculations.
Transcribed Image Text:### Analysis of Poll Results on Healthcare as the Most Important Issue A CBS News/New York Times poll surveyed 990 Americans to determine their views on the most important problem facing the U.S. health care system. Out of those surveyed, 30 respondents identified health care as the top issue. We can estimate the true proportion of Americans holding this view using a 96% confidence interval. #### Margin of Error - **E** = 0.0112 #### Interval Calculation To calculate the confidence interval, we adjust the observed proportion by the margin of error. - Calculated Interval: \[ 0.0303 - 0.0112 < p < 0.0303 + 0.0112 \] \[ 0.0191 < p < 0.0415 \] Expressed in percentage, the interval is: - **1.91% < p < 4.15%** This interval estimates that between 1.91% and 4.15% of Americans believe health care is the most important problem. #### Graph Explanation A table is provided to support the calculations: - **Z Estimate of a Proportion**: - **Successes**: 30 - **Sample Size (N)**: 990 - **Standard Error (SE)**: 0.0054 - **Lower Limit**: 0.0191 - **Upper Limit**: 0.0415 - **Interval**: 0.0303 ± 0.0112 The results are visually supported with a structured data table to ensure clarity in understanding the confidence interval calculations.
Expert Solution
Step 1: Information given is

sample size(n)=990

x=30

confidence level=96%

sample proportion(straight p with hat on top)=straight x over straight n equals 30 over 990 equals 0.0303030303

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