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Ch. 6 - Confidence Intervals
Larson - Elementary Statistics: Picturing the World 8th Edition
Larson8th EditionElementary Statistics: Picturing the WorldISBN: 9780137493470당신이 사용하는 게 아니라요?교과서 변경
모든 교과서Larson 8th EditionCh. 6 - Confidence Intervals문제 6.Tech.3b
6장, 문제 6.Tech.3b

Since 1935, the Gallup Organization has conducted public opinion polls in the United States and around the world. The table shows the results of Gallup’s World Affairs Poll of 2021, in which 1021 U.S. adults were polled. The remaining percentages not shown in the results are adults who were not sure.
Random number generation interface displaying parameters for a binomial distribution with p-value 0.54 and 1537 trials.
b. What was the greatest value you obtained for p^?

검증된 단계별 안내
1
Step 1: Understand the problem. The question asks for the greatest value of p^ (sample proportion) obtained from the Gallup World Affairs Poll of 2021. The image provides parameters for a binomial distribution simulation, which can help analyze probabilities or proportions.
Step 2: Recall the formula for the sample proportion p^: p^ = x/n, where x is the number of successes and n is the total number of trials. In this case, n = 1021 (the number of U.S. adults polled).
Step 3: Analyze the image. The Random Number Generation tool is set to simulate a binomial distribution with p = 0.54 (probability of success) and 1537 trials. However, this simulation is unrelated to the actual poll data, which involves 1021 adults. Focus on the poll data for calculating p^.
Step 4: To find the greatest value of p^, identify the category with the highest number of successes (x) from the poll data. If the data is not explicitly provided, assume the highest percentage corresponds to the greatest p^.
Step 5: Calculate the greatest p^ using the formula p^ = x/n, where x corresponds to the highest percentage of responses multiplied by n (1021). Ensure to convert the percentage into a decimal before multiplying.

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Proportion Estimate (p^)

The proportion estimate, denoted as p^ (p-hat), represents the sample proportion of a certain characteristic in a population. It is calculated by dividing the number of successes (individuals with the characteristic) by the total number of observations in the sample. In the context of polling, p^ indicates the percentage of respondents who expressed a particular opinion.
추천 영상:
가이드 코스
08:09
Difference in Proportions: Confidence Intervals

Binomial Distribution

The binomial distribution is a probability distribution that describes the number of successes in a fixed number of independent Bernoulli trials, each with the same probability of success. It is characterized by two parameters: the number of trials (n) and the probability of success (p). This distribution is useful for modeling scenarios like polling, where outcomes can be classified as success or failure.
추천 영상:
가이드 코스
03:28
Mean & Standard Deviation of Binomial Distribution

Random Sampling

Random sampling is a technique used to select a subset of individuals from a larger population, ensuring that each individual has an equal chance of being chosen. This method helps to obtain a representative sample, which is crucial for making valid inferences about the population. In the context of the Gallup poll, random sampling ensures that the opinions of the 1021 U.S. adults reflect the broader population's views.
추천 영상:
가이드 코스
04:17
Simple Random Sampling
관련 실천
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a. No preliminary estimate is available. Find the minimum sample size needed.

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a. Find the point estimate for the population proportion.

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Since 1935, the Gallup Organization has conducted public opinion polls in the United States and around the world. The table shows the results of Gallup’s World Affairs Poll of 2021, in which 1021 U.S. adults were polled. The remaining percentages not shown in the results are adults who were not sure.

[IMAGE]

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c. Would it be unusual for the population mean to be under 575? Explain.

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Since 1935, the Gallup Organization has conducted public opinion polls in the United States and around the world. The table shows the results of Gallup’s World Affairs Poll of 2021, in which 1021 U.S. adults were polled. The remaining percentages not shown in the results are adults who were not sure.

Use technology to find a 95% confidence interval for the population proportion of adults who

a. view foreign trade as an economic opportunity.

36
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