AP Statistics Flashcards: Justifying a Claim About the Difference of Two Means Based on a Confidence Interval
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What does a confidence interval for a difference of means provide?
A confidence interval for a difference of means provides a range of plausible values for the true difference between two population means, which can be used to support a claim.
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What does a confidence interval for a difference of means provide?
A confidence interval for a difference of means provides a range of plausible values for the true difference between two population means, which can be used to support a claim.
Provide the standard sentence structure for interpreting a confidence interval for a difference of two means.
We are C% confident that the interval from [lower bound] to [upper bound] captures the true difference in the means of [population 1] and [population 2].
What is the meaning of the confidence *level* (e.g., 95%) in the context of repeated sampling?
In repeated sampling, the stated confidence level (C%) is the approximate percentage of confidence intervals that will capture the true difference of the population means.
Interpret the phrase 'plausible values' in the context of a confidence interval for a difference of means.
Plausible values are all the values contained within the calculated confidence interval, any of which could represent the true difference between the two population means.
What is the effect of increasing sample size on the width of a confidence interval for the difference of two means?
The width of the confidence interval for the difference of two means tends to decrease as sample sizes increase.
A 99% confidence interval for the difference in mean scores (Group A - Group B) is (-5.2, -1.8). What claim can be made?
Since all plausible values in the interval are negative, we can justify the claim that the mean score for Group A is lower than the mean score for Group B.
How does sample size relate to the precision of the estimate for the difference of two means?
As sample sizes increase, the confidence interval width tends to decrease, which corresponds to a more precise estimate of the true difference of the population means.
If a confidence interval for a difference of population means (μ₁ - μ₂) contains only positive values, what claim does this support?
This supports the claim that the first population mean (μ₁) is greater than the second population mean (μ₂), as all plausible values for the difference are greater than zero.
If a confidence interval for a difference of population means (μ₁ - μ₂) contains zero, what claim can be justified?
If the interval contains zero, it is a plausible value for the difference, so we cannot justify a claim of a significant difference between the two population means.
How do you justify a claim based on a confidence interval for a difference of population means?
A claim is justified by determining if the plausible values within the confidence interval are consistent with the claim being made about the difference between the two population means.
What two specific contexts must be referenced when interpreting a confidence interval for a difference of two means?
An interpretation for a confidence interval for the difference of two means must reference both the samples used and the populations the inference is about.