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Questions and Answers
What is the primary purpose of a confidence interval?
What is the primary purpose of a confidence interval?
What is the relationship between the confidence level and the margin of error?
What is the relationship between the confidence level and the margin of error?
What is the formula for a one-sample confidence interval?
What is the formula for a one-sample confidence interval?
What is the main difference between a one-sample and two-sample confidence interval?
What is the main difference between a one-sample and two-sample confidence interval?
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What is the correct interpretation of a 95% confidence interval?
What is the correct interpretation of a 95% confidence interval?
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What is a common misconception about confidence intervals?
What is a common misconception about confidence intervals?
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What calculator function would you use to calculate a confidence interval for a population proportion?
What calculator function would you use to calculate a confidence interval for a population proportion?
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What is the effect of increasing the confidence level on the interval width?
What is the effect of increasing the confidence level on the interval width?
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What is the purpose of the critical value in a confidence interval calculation?
What is the purpose of the critical value in a confidence interval calculation?
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What is a key assumption underlying confidence interval calculations?
What is a key assumption underlying confidence interval calculations?
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Study Notes
Confidence Intervals
Definition
- A confidence interval is a range of values within which a population parameter is likely to lie
- It is a measure of the amount of uncertainty associated with a sample statistic
Key Concepts
- Confidence Level: The probability that the interval contains the true population parameter (e.g. 95%)
- Margin of Error: The maximum amount by which the sample statistic may differ from the true population parameter
- Interval Width: The difference between the upper and lower bounds of the interval
Types of Confidence Intervals
-
One-Sample Confidence Interval
- Used to estimate a population mean (μ) or proportion (p)
- Formula:
CI = sample statistic ± (critical value × standard error)
-
Two-Sample Confidence Interval
- Used to compare the means or proportions of two populations
- Formula:
CI = (sample statistic 1 - sample statistic 2) ± (critical value × standard error)
Interpretation
- 95% Confidence Interval: There is a 95% probability that the true population parameter lies within the interval
- Do not interpret the confidence interval as a probability statement about the sample statistic
Common Misconceptions
- Do not say that the true population parameter has a 95% probability of lying within the interval
- Do not assume that the interval is a range of values within which the sample statistic will lie
Calculator Functions
-
TI-83/84 Calculator: Use the
1-PropZIntorTIntervalfunctions to calculate confidence intervals - Other Calculators: Check your calculator's manual for equivalent functions
Confidence Intervals
- A range of values within which a population parameter is likely to lie, measuring the uncertainty associated with a sample statistic
Key Concepts
- Confidence Level: The probability that the interval contains the true population parameter, e.g., 95%
- Margin of Error: The maximum amount by which the sample statistic may differ from the true population parameter
- Interval Width: The difference between the upper and lower bounds of the interval
Types of Confidence Intervals
-
One-Sample Confidence Interval: Estimates a population mean (μ) or proportion (p) using the formula:
CI = sample statistic ± (critical value × standard error) -
Two-Sample Confidence Interval: Compares the means or proportions of two populations using the formula:
CI = (sample statistic 1 - sample statistic 2) ± (critical value × standard error)
Interpretation
- A 95% Confidence Interval means there is a 95% probability that the true population parameter lies within the interval
- Do not interpret the confidence interval as a probability statement about the sample statistic
Important Notes
- Common Misconceptions: Do not say the true population parameter has a 95% probability of lying within the interval, or assume the interval is a range of values within which the sample statistic will lie
Calculator Functions
-
TI-83/84 Calculator: Use the
1-PropZIntorTIntervalfunctions to calculate confidence intervals - Other Calculators: Check your calculator's manual for equivalent functions
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Description
Learn about the concepts of confidence intervals, including confidence level, margin of error, and interval width, in statistics and research.
