Overpriced Apples - In a poll of 228 college students, 176 believe that iPhones are overpriced. You are interested in estimating the true proportion of college students who think iPhones are overpriced. Round all calculated answers to 4 decimal places where appropriate. 1. Using the information from the poll, construct a 95% confidence interval for the true proportion of college students who think iPhones are overpriced. 0.7175 0.8264 2. How many college students should you survey to estimate the true proportion of college students who think iPhone are overpriced, with 95% confidence and a margin of error of no more than 4.5%? Use the information from the poll for a planning value for p*. n = 333
Overpriced Apples - In a poll of 228 college students, 176 believe that iPhones are overpriced. You are interested in estimating the true proportion of college students who think iPhones are overpriced. Round all calculated answers to 4 decimal places where appropriate. 1. Using the information from the poll, construct a 95% confidence interval for the true proportion of college students who think iPhones are overpriced. 0.7175 0.8264 2. How many college students should you survey to estimate the true proportion of college students who think iPhone are overpriced, with 95% confidence and a margin of error of no more than 4.5%? Use the information from the poll for a planning value for p*. n = 333
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I need help with question 2 and 3 plz.
![### Overpriced Apples: Estimating Proportion of College Students Who Think iPhones are Overpriced
In a poll of 228 college students, 176 believe that iPhones are overpriced. You are interested in estimating the true proportion of college students who think iPhones are overpriced.
Below are the calculations and analyses involved, rounded to four decimal places where appropriate.
#### 1. Constructing a 95% Confidence Interval
**Question:**
Using the information from the poll, construct a 95% confidence interval for the true proportion of college students who think iPhones are overpriced.
**Answer:**
The 95% confidence interval is calculated to be:
\[ (0.7175, 0.8264) \]
#### 2. Sample Size Calculation for a Desired Margin of Error
**Question:**
How many college students should you survey to estimate the true proportion of college students who think iPhones are overpriced, with 95% confidence and a margin of error of no more than 4.5%? Use the information from the poll for a planning value for \( p^* \).
**Answer:**
Based on the calculations, you should survey:
\[ n = 333 \]
#### 3. Interpretation of Confidence Interval
**Scenario:**
Janae is a statistics student who conducts a similar survey at her college. She constructs a 90% confidence interval for the true proportion of college students at her college who believe that iPhones are overpriced, which is found to be \( (0.354, 0.492) \).
**Question:**
Which of the following statements are appropriate interpretations of the confidence interval? Select all that apply.
**Choices:**
- A. We expect any sample proportion to be in the interval 90% of the time, on average.
- B. In repeated sampling, we can expect 90% of the intervals we construct to contain the true proportion of college students at Janae's college who believe iPhones are overpriced.
- C. We can be 90% confident that, on average, a new sample of the same size will give a sample proportion within the lower and upper bounds of the confidence interval.
- D. We can be 90% confident that the true proportion of college students at Janae's college who believe iPhones are overpriced is contained in the interval constructed above.
**Correct Answer:**
- ☑ D. We can be 90% confident that the true proportion](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9a233757-ff48-478f-9071-7d7d23b994ff%2F0bfa0cd8-d0d6-488f-ac57-1bdb9af0b064%2Fk4tbcm4_processed.png&w=3840&q=75)
Transcribed Image Text:### Overpriced Apples: Estimating Proportion of College Students Who Think iPhones are Overpriced
In a poll of 228 college students, 176 believe that iPhones are overpriced. You are interested in estimating the true proportion of college students who think iPhones are overpriced.
Below are the calculations and analyses involved, rounded to four decimal places where appropriate.
#### 1. Constructing a 95% Confidence Interval
**Question:**
Using the information from the poll, construct a 95% confidence interval for the true proportion of college students who think iPhones are overpriced.
**Answer:**
The 95% confidence interval is calculated to be:
\[ (0.7175, 0.8264) \]
#### 2. Sample Size Calculation for a Desired Margin of Error
**Question:**
How many college students should you survey to estimate the true proportion of college students who think iPhones are overpriced, with 95% confidence and a margin of error of no more than 4.5%? Use the information from the poll for a planning value for \( p^* \).
**Answer:**
Based on the calculations, you should survey:
\[ n = 333 \]
#### 3. Interpretation of Confidence Interval
**Scenario:**
Janae is a statistics student who conducts a similar survey at her college. She constructs a 90% confidence interval for the true proportion of college students at her college who believe that iPhones are overpriced, which is found to be \( (0.354, 0.492) \).
**Question:**
Which of the following statements are appropriate interpretations of the confidence interval? Select all that apply.
**Choices:**
- A. We expect any sample proportion to be in the interval 90% of the time, on average.
- B. In repeated sampling, we can expect 90% of the intervals we construct to contain the true proportion of college students at Janae's college who believe iPhones are overpriced.
- C. We can be 90% confident that, on average, a new sample of the same size will give a sample proportion within the lower and upper bounds of the confidence interval.
- D. We can be 90% confident that the true proportion of college students at Janae's college who believe iPhones are overpriced is contained in the interval constructed above.
**Correct Answer:**
- ☑ D. We can be 90% confident that the true proportion
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