Large Counts Condition
Definition
The large counts condition, also known as the "success-failure" condition, is used when applying certain statistical methods to categorical data. It states that for these methods to be valid, both the number of successes and failures must be at least 10.
Analogy
Imagine you are flipping a fair coin 100 times. To apply certain statistical methods, we need to have a sufficient number of heads (successes) and tails (failures). If we only had 2 heads and 98 tails, it would not meet the large counts condition. We need a balanced distribution of outcomes for our analysis to be valid.
Related terms
Binomial Distribution: The binomial distribution is a probability distribution that describes the number of successes in a fixed number of independent Bernoulli trials.
Hypothesis Testing: Hypothesis testing is a statistical method used to make inferences about population parameters based on sample data.
Confidence Interval: A confidence interval is an estimate range within which we can reasonably expect the true population parameter to fall with a certain level of confidence. The large counts condition plays a role in determining whether certain methods can be applied when constructing confidence intervals.
"Large Counts Condition" appears in:
Study guides (6)
AP Statistics - 5.5 Sampling Distributions for Sample Proportions
AP Statistics - 6.1 Introducing Statistics: Why Be Normal?
AP Statistics - 6.3 Justifying a Claim Based on a Confidence Interval for a Population Proportion
AP Statistics - 6.4 Setting Up a Test for a Population Proportion
AP Statistics - 6.8 Confidence Intervals for the Difference of Two Proportions
AP Statistics - 6.10 Setting Up a Test for the Difference of Two Population Proportions
Additional resources (2)
Practice Questions (8)
If a sample meets the Large Counts Condition, which of the following statistical techniques can we use to make inferences about the population proportion?
If the sample proportion is 0.8, what is the minimum size of the sample in order for the Large Counts Condition to be satisfied?
If a sample does not meet the Large Counts Condition and no other information is known about the population distribution, what can be said about the sampling distribution’s shape?
If a sample is of size 250, what should be the minimum number of successes to satisfy the Large Counts Condition?
What should be the minimum number of failures in a sample of size 300 to satisfy the Large Counts Condition?
If the sample proportion is 0.27, what is the minimum size of the sample in order for the Large Counts Condition to be satisfied?
In the hockey players example, what would be the conclusion if the Large Counts Condition was not satisfied?
Why do we need to verify the Large Counts Condition to use the normal curve in sampling distributions?
Resources
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