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- 6.2 Confidence Interval For The Mean (σ Unknown)
6.2 Confidence Interval for the Mean (σ unknown)
Flashcard
•
Mathematics
•
9th - 12th Grade
•
Hard
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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 value of an unknown population parameter, such as the mean, with a specified level of confidence.
2.
FLASHCARD QUESTION
Front
What does it mean when we say a confidence interval is 95%?
Back
A 95% confidence interval means that if we were to take many samples and build a confidence interval from each sample, approximately 95% of those intervals would contain the true population mean.
3.
FLASHCARD QUESTION
Front
What is the formula for calculating a confidence interval for the mean when the population standard deviation is unknown?
Back
The formula is: CI = x̄ ± t*(s/√n), where x̄ is the sample mean, t is the t-score from the t-distribution, s is the sample standard deviation, and n is the sample size.
4.
FLASHCARD QUESTION
Front
What is the t-distribution?
Back
The t-distribution is a probability distribution that is used to estimate population parameters when the sample size is small and/or the population standard deviation is unknown.
5.
FLASHCARD QUESTION
Front
How do you determine the t-score for a confidence interval?
Back
The t-score can be determined using a t-table, which requires the desired confidence level and the degrees of freedom (df = n - 1, where n is the sample size).
6.
FLASHCARD QUESTION
Front
What is the significance of degrees of freedom in confidence intervals?
Back
Degrees of freedom are used in statistical calculations to account for the number of independent values in a sample. In confidence intervals, it affects the t-score used.
7.
FLASHCARD QUESTION
Front
What is the relationship between sample size and confidence interval width?
Back
As the sample size increases, the width of the confidence interval decreases, leading to a more precise estimate of the population mean.
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