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 are the differences between the 10% condition and random assignment in the context of independence for two-sample z-intervals?
10% Condition: Population size is at least 10 times the sample size. | Random Assignment: Used in experiments to ensure independence between treatment groups.
What are the differences between a point estimate and a confidence interval?
Point Estimate: A single value estimate of a population parameter. | Confidence Interval: A range of values likely to contain the population parameter.
What are the differences between successes and failures in the context of the large counts condition?
Successes: The number of observations that meet a certain criteria. | Failures: The number of observations that do not meet a certain criteria.
What are the differences between p̂1 and p̂2 in the context of two sample z-intervals?
p̂1: The sample proportion for group 1. | p̂2: The sample proportion for group 2.
What are the differences between a Z-test and a Z-interval?
Z-test: Used to test a hypothesis about a population parameter. | Z-interval: Used to estimate a population parameter with a certain level of confidence.