Finding p^ and q^ In Exercises 3–6, let p be the population proportion for the situation. Find point estimates of p and q.
Private Internet Browsing In a survey of 4272 U.S. adults, 1025 knew that private browsing mode only prevents someone using the same computer from seeing one’s online activities. (Adapted from Pew Research Center)

검증된 단계별 안내

Identify the given values in the problem: The total sample size (n) is 4272, and the number of successes (x) is 1025. A 'success' in this context refers to a respondent knowing that private browsing mode only prevents someone using the same computer from seeing one’s online activities.

Recall the formula for the sample proportion (p̂), which is the point estimate of the population proportion (p). The formula is:

p^= \frac{x}{n}

. Here, x is the number of successes, and n is the total sample size.

Substitute the given values into the formula for p̂:

p^= \frac{1025}{4272}

. This will give the point estimate of the population proportion.

To find q̂, which is the complement of p̂, use the formula:

q^= 1 - p^

. This represents the proportion of respondents who do not know that private browsing mode only prevents someone using the same computer from seeing one’s online activities.

Substitute the calculated value of p̂ into the formula for q̂ to find the complement proportion. This completes the calculation of both p̂ and q̂.

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주요 개념

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

Population Proportion

The population proportion, denoted as p, represents the fraction of a population that possesses a certain characteristic. In this context, it refers to the proportion of U.S. adults who understand the function of private browsing mode. It is calculated by dividing the number of individuals with the characteristic by the total number of individuals surveyed.

Point Estimate

A point estimate is a single value that serves as an approximation of a population parameter. In this case, p^ (p-hat) is the point estimate of the population proportion p, calculated from sample data. It provides a quick estimate of the true population proportion based on the observed sample.

Complement of a Proportion

The complement of a proportion, denoted as q, represents the proportion of the population that does not have the characteristic of interest. It is calculated as q = 1 - p. In this scenario, q would indicate the proportion of U.S. adults who do not understand the private browsing mode, providing a complete view of the population's knowledge.