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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1:35 minutes

Problem 6.3.9

Textbook Question

In Exercises 7–10, use the confidence interval to find the margin of error and the sample proportion.
(0.512, 0.596)

Verified step by step guidance

Identify the given confidence interval, which is (0.512, 0.596). The lower bound is 0.512, and the upper bound is 0.596.

To find the margin of error (E), use the formula:

E = \frac{\text{Upper Bound} - \text{Lower Bound}}{2}

. Substitute the values of the upper and lower bounds into this formula.

To find the sample proportion (p̂), use the formula:

\hat{p} = \frac{\text{Upper Bound} + \text{Lower Bound}}{2}

. Substitute the values of the upper and lower bounds into this formula.

Perform the subtraction and division in the margin of error formula to calculate E.

Perform the addition and division in the sample proportion formula to calculate p̂.

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Key Concepts

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

Confidence Interval

A confidence interval is a range of values, derived from sample statistics, that is likely to contain the true population parameter. It is expressed as an interval (e.g., (0.512, 0.596)) and is associated with a confidence level, typically 95% or 99%. This means that if we were to take many samples and construct confidence intervals for each, a certain percentage of those intervals would contain the true parameter.

Margin of Error

The margin of error quantifies the uncertainty associated with a sample estimate. It is calculated as half the width of the confidence interval, representing the maximum expected difference between the sample proportion and the true population proportion. In the given interval (0.512, 0.596), the margin of error can be found by subtracting the lower limit from the upper limit and dividing by two.

Sample Proportion

The sample proportion is the ratio of the number of successes in a sample to the total number of observations in that sample. It is denoted as 'p̂' and provides an estimate of the true population proportion. In the context of the confidence interval (0.512, 0.596), the sample proportion can be calculated as the midpoint of the interval, which gives a point estimate of the population proportion.

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In Exercises 7–10, use the confidence interval to find the margin of error and the sample proportion.(0.512, 0.596)

Key Concepts

Confidence Interval

Margin of Error

Sample Proportion

Watch next

In Exercises 7–10, use the confidence interval to find the margin of error and the sample proportion.
(0.512, 0.596)