Confidence Intervals for Proportions

Confidence Intervals for Proportions

Assessment

Flashcard

Mathematics

11th - 12th Grade

Practice Problem

Hard

Created by

Wayground Content

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15 questions

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1.

FLASHCARD QUESTION

Front

What is a confidence interval?

Back

A confidence interval is a range of values, derived from a data set, that is likely to contain the true value of an unknown population parameter, with a specified level of confidence.

2.

FLASHCARD QUESTION

Front

What does a 90% confidence level mean?

Back

A 90% confidence level means that if we were to take many samples and build a confidence interval from each sample, approximately 90% of those intervals would contain the true population parameter.

3.

FLASHCARD QUESTION

Front

How do you calculate a confidence interval for a proportion?

Back

To calculate a confidence interval for a proportion, use the formula: CI = p̂ ± z* × √(p̂(1-p̂)/n), where p̂ is the sample proportion, z* is the critical value for the desired confidence level, and n is the sample size.

4.

FLASHCARD QUESTION

Front

What is the critical value (z*) for a 90% confidence interval?

Back

The critical value (z*) for a 90% confidence interval is approximately 1.645.

5.

FLASHCARD QUESTION

Front

What is the formula for the margin of error in a confidence interval for proportions?

Back

The margin of error (ME) is calculated as ME = z* × √(p̂(1-p̂)/n).

6.

FLASHCARD QUESTION

Front

How do you interpret a confidence interval?

Back

A confidence interval provides a range of values that is believed to contain the true population parameter. For example, if the CI is (0.621, 0.759), we believe the true proportion lies within this range.

7.

FLASHCARD QUESTION

Front

What is the sample proportion (p̂)?

Back

The sample proportion (p̂) is the number of successes (e.g., individuals with a certain characteristic) divided by the total number of observations in the sample.

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