
Confidence Intervals for Means
Flashcard
•
Mathematics
•
11th Grade - University
•
Practice Problem
•
Hard
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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. It is used to estimate the uncertainty around a sample statistic.
2.
FLASHCARD QUESTION
Front
What does the margin of error represent in a confidence interval?
Back
The margin of error represents the maximum expected difference between the true population parameter and a sample estimate. It quantifies the uncertainty in the estimate.
3.
FLASHCARD QUESTION
Front
How do you calculate the margin of error for a confidence interval?
Back
Margin of Error = Critical Value (t* or z*) * (Standard Deviation / √n), where n is the sample size.
4.
FLASHCARD QUESTION
Front
What is the critical value (t*) in a confidence interval?
Back
The critical value (t*) is a factor used to compute the margin of error, based on the desired confidence level and the sample size. It is derived from the t-distribution.
5.
FLASHCARD QUESTION
Front
What is the difference between a z-interval and a t-interval?
Back
A z-interval is used when the population standard deviation is known or the sample size is large (n > 30), while a t-interval is used when the population standard deviation is unknown and the sample size is small (n ≤ 30).
6.
FLASHCARD QUESTION
Front
What is the formula for a confidence interval for the mean?
Back
Confidence Interval = Sample Mean ± Margin of Error.
7.
FLASHCARD QUESTION
Front
What is the significance of the sample size (n) in confidence intervals?
Back
A larger sample size reduces the margin of error and increases the precision of the confidence interval, leading to a more reliable estimate of the population parameter.
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