All Flashcards
What is the formula for the standard error (SE) in a two-sample z-interval?
SE = √(p̂1(1-p̂1)/n1 + p̂2(1-p̂2)/n2)
What is the formula for a two-sample z-interval?
(p̂1 - p̂2) ± z* * √(p̂1(1-p̂1)/n1 + p̂2(1-p̂2)/n2)
How do you calculate the point estimate for the difference of two proportions?
p̂1 - p̂2
What is the formula for the lower bound of a two-sample z-interval?
(p̂1 - p̂2) - z* * √(p̂1(1-p̂1)/n1 + p̂2(1-p̂2)/n2)
What is the formula for the upper bound of a two-sample z-interval?
(p̂1 - p̂2) + z* * √(p̂1(1-p̂1)/n1 + p̂2(1-p̂2)/n2)
Explain the concept of the Randomness condition for two-sample z-intervals.
Both samples must be random samples to generalize findings to the population.
Explain the concept of the Independence condition for two-sample z-intervals.
Each population should be at least 10 times larger than its respective sample size (10% condition), or random assignment is used.
Explain the concept of the Normality condition (Large Counts) for two-sample z-intervals.
Both samples must have at least 10 expected successes and 10 expected failures: n₁p̂₁ ≥ 10, n₁(1-p̂₁) ≥ 10, n₂p̂₂ ≥ 10, and n₂(1-p̂₂) ≥ 10.
Explain the importance of checking conditions before constructing a two-sample z-interval.
Checking conditions ensures the validity of the inference and that the results can be reliably generalized.
Explain how to interpret a two-sample z-interval.
We are [confidence level]% confident that the true difference in [context] is between [lower bound] and [upper bound].
What is a two-sample z-interval?
A confidence interval used to estimate the difference between two population proportions for a categorical variable.
Define point estimate in the context of two-sample z-intervals.
The difference between the two sample proportions: p̂1 - p̂2.
What is the margin of error in a two-sample z-interval?
The 'buffer zone' around the point estimate, calculated using the critical value (z-score) and standard error.
Define standard error (SE) in the context of two-sample z-intervals.
A measure of the variability of the difference between two sample proportions.
What does it mean if a two-sample z-interval contains 0?
It suggests there might not be a significant difference between the two population proportions.