AP Statistics Flashcards: Justifying a Claim About a Population Mean Based on a Confidence Interval
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What does a confidence interval for a population mean provide in terms of a claim?
A confidence interval for a population mean provides a range of plausible values that can be used to support or reject a claim.
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What does a confidence interval for a population mean provide in terms of a claim?
A confidence interval for a population mean provides a range of plausible values that can be used to support or reject a claim.
Plausible Values
The range of values for the population mean, provided by the confidence interval, that can be used to support a claim.
How do you justify a claim about a population mean using a confidence interval?
If the claimed value of the population mean falls within the calculated confidence interval, the claim is justified because it is a plausible value.
Confidence Interval for a Matched Pairs Mean
An interval providing plausible values for the true mean of the differences between paired data points.
What is the relationship between sample size and the width of a confidence interval for a mean?
The width of a confidence interval for a population mean tends to decrease as the sample size increases.
If you want to make your confidence interval narrower without changing the confidence level, what must you do?
To create a narrower confidence interval, you must increase the sample size.
What is the relationship between the confidence level and the width of a confidence interval for a mean?
For a given sample, the width of the confidence interval for a mean increases as the confidence level increases.
What is the specific mathematical relationship between interval width and sample size (n) for a single mean?
The width of the confidence interval for a single mean is proportional to 1 divided by the square root of n (1/√n).
A 99% confidence interval for the mean weight of a product is (15.8, 16.1) oz. Does this interval support a claim that the true mean weight is 15.5 oz?
No, this interval does not support the claim because 15.5 oz is not a plausible value as it falls outside the interval (15.8, 16.1).
In a matched pairs experiment, how would a confidence interval for the mean difference support a claim of 'no effect'?
If the value 0 is contained within the confidence interval for the mean difference, it is a plausible value, which supports the claim of no effect or no difference.
How does the margin of error for a population mean change as the confidence level increases?
As the confidence level increases, the margin of error also increases, which results in a wider confidence interval.
What is the fundamental truth about any single, calculated confidence interval?
A confidence interval for a population mean either contains the true population mean, or it does not.
How does the margin of error for a population mean change as the sample size increases?
As the sample size increases, the margin of error decreases, which results in a narrower confidence interval.
Why is a 99% confidence interval wider than a 90% confidence interval calculated from the same data?
A higher confidence level requires a wider interval to be more certain that it has captured the true population mean.
Confidence Interval for a Population Mean
An interval estimate, based on sample data, that provides a range of plausible values for an unknown population mean.
A 95% confidence interval for the mean daily screen time is (3.1, 4.5) hours. Does this interval support a claim that the true mean is 4 hours?
Yes, this interval supports the claim because 4 hours is a plausible value contained within the interval (3.1, 4.5).
What is the standard interpretation of a C% confidence level for a population mean?
We are C% confident that the interval we calculated captures the true population mean.
What is the trade-off when you increase the confidence level for an interval based on the same sample?
Increasing the confidence level makes the interval wider, which means you are more confident but your estimate is less precise.
What two key components must be referenced in a proper interpretation of a confidence interval for a mean?
An interpretation of a confidence interval for a mean should reference the sample data used and the population parameter being estimated.