(b) Estimate the sample size needed if no estimate of p is available. A sample of adults is needed to obtain an 80% confidence interval with a margin of error of 0.05. X S

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### Constructing an 80% Confidence Interval for Economic Perceptions

To understand public opinion on whether economic conditions are improving, a pollster aims to construct an 80% confidence interval for the proportion of adults who believe the economy is getting better. Below are the steps for calculating the necessary sample size under different scenarios.

#### Part 1 of 2
(a) **Given Estimate:**
A poll taken in July 2010 estimates this proportion to be 0.28. Using this estimate, what sample size is needed so that the confidence interval will have a margin of error of 0.05?

**Solution:**
- A sample of **133** adults is needed to obtain an 80% confidence interval with a margin of error of 0.05.

An interactive bar indicated is labeled "Part: 1/2".

#### Part 2 of 2
(b) **Without Prior Estimate:**
Estimate the sample size needed if no estimate of \( p \) is available.

**Solution:**
- A sample of \[ \_\_\_ \] adults is needed to obtain an 80% confidence interval with a margin of error of 0.05.

Users will need to input the appropriate value based on their calculations, with a temporary placeholder indicating where the sample size should be entered.

**Graphical Elements:**
- There is a progress bar indicating the user is on "Part: 1/2".
- Buttons for actions such as "Save For Later," "Submit Assignment," and "Check" are included at the bottom.

This educational exercise demonstrates the steps for determining the required sample size for constructing confidence intervals under different conditions, with practical applications in understanding public opinion on economic trends.
Transcribed Image Text:### Constructing an 80% Confidence Interval for Economic Perceptions To understand public opinion on whether economic conditions are improving, a pollster aims to construct an 80% confidence interval for the proportion of adults who believe the economy is getting better. Below are the steps for calculating the necessary sample size under different scenarios. #### Part 1 of 2 (a) **Given Estimate:** A poll taken in July 2010 estimates this proportion to be 0.28. Using this estimate, what sample size is needed so that the confidence interval will have a margin of error of 0.05? **Solution:** - A sample of **133** adults is needed to obtain an 80% confidence interval with a margin of error of 0.05. An interactive bar indicated is labeled "Part: 1/2". #### Part 2 of 2 (b) **Without Prior Estimate:** Estimate the sample size needed if no estimate of \( p \) is available. **Solution:** - A sample of \[ \_\_\_ \] adults is needed to obtain an 80% confidence interval with a margin of error of 0.05. Users will need to input the appropriate value based on their calculations, with a temporary placeholder indicating where the sample size should be entered. **Graphical Elements:** - There is a progress bar indicating the user is on "Part: 1/2". - Buttons for actions such as "Save For Later," "Submit Assignment," and "Check" are included at the bottom. This educational exercise demonstrates the steps for determining the required sample size for constructing confidence intervals under different conditions, with practical applications in understanding public opinion on economic trends.
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