Table of contents

1. Intro to Stats and Collecting Data55m
2. Describing Data with Tables and Graphs1h 55m
3. Describing Data Numerically1h 45m
4. Probability2h 16m
5. Binomial Distribution & Discrete Random Variables2h 33m
6. Normal Distribution and Continuous Random Variables1h 38m
7. Sampling Distributions & Confidence Intervals: Mean1h 53m
8. Sampling Distributions & Confidence Intervals: Proportion1h 12m
- Sampling Distribution of Sample Proportion
  29m
- Confidence Intervals for Population Proportion
  42m
9. Hypothesis Testing for One Sample2h 19m
10. Hypothesis Testing for Two Samples3h 22m
11. Correlation1h 6m
12. Regression1h 4m
13. Chi-Square Tests & Goodness of Fit1h 20m
14. ANOVA1h 0m

8. Sampling Distributions & Confidence Intervals: Proportion

Confidence Intervals for Population Proportion

Statistics

8. Sampling Distributions & Confidence Intervals: Proportion

Confidence Intervals for Population Proportion

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1:24 minutes

Problem 6.3.6

Textbook Question

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)

Verified step by step guidance

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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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

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.

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Textbook Question

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Textbook Question

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Textbook Question

Finding p^ and q^ In Exercises 3–6, let p be the population proportion for the situation. Find point estimates of p and q.

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Textbook Question

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(0.512, 0.596)

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Textbook Question

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Textbook Question

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Textbook Question

Constructing Confidence Intervals In Exercises 13 and 14, construct a 99% confidence interval for the population proportion. Interpret the results.

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