1 A poll conducted by the UC Berkeley Institute of Govermmental Studies in 2019 found that of 4527 respondents said they considered moving out of the state.
a) Are the conditions for constructing a confidence interval met? Select all that apply.
A. Yes, all assumptions and conditions are met.
B. No, because there are less than 10 expected “successes” and 10 expected “failures.”
C. No, because there are at least 10 expected “successes” and 10 expected “failures.”
D. No, because the sample is not a simple random sample.
E. No, because the sample is greater than of the population.
F. No, because the sample is a simple random sample.
G. No, because the sample is less than of the population.

Ask by Nguyen Cole. in the United States

Mar 31,2025

Question

1 A poll conducted by the UC Berkeley Institute of Govermmental Studies in 2019 found that of 4527 respondents said they considered moving out of the state.
a) Are the conditions for constructing a confidence interval met? Select all that apply.
A. Yes, all assumptions and conditions are met.
B. No, because there are less than 10 expected “successes” and 10 expected “failures.”
C. No, because there are at least 10 expected “successes” and 10 expected “failures.”
D. No, because the sample is not a simple random sample.
E. No, because the sample is greater than of the population.
F. No, because the sample is a simple random sample.
G. No, because the sample is less than of the population.

Ask by Nguyen Cole. in the United States

Mar 31,2025

UpStudy AI · Accepted Answer

1. Define the "success" as a respondent considering moving out-of-state. The sample proportion is provided as  
   $$
   \hat p = 0.518.
   $$

2. The conditions for constructing a confidence interval for a proportion include:
   - The sample is obtained via a simple random sample.
   - The observations are independent.
   - The sample size is large enough so that the expected numbers of successes and failures are both at least $$10$$.

3. For this poll with $$ n = 4527 $$:
   - Expected successes:  
     $$
     n\hat p = 4527 \times 0.518 \approx 2347,
     $$
   - Expected failures:  
     $$
     n(1-\hat p) = 4527 \times (1 - 0.518) \approx 2180.
     $$
   Both values are well above $$10$$.

4. Provided the poll was conducted properly as a random sample, all the conditions are met.

5. The correct answer is:

$$
\boxed{\text{A. Yes, all assumptions and conditions are met.}}
$$
All conditions for constructing a confidence interval are met. **Answer:** A. Yes, all assumptions and conditions are met.

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