Consider the patient data in Example 2-8. Suppose that...

Consider the patient data in Example $2-8$. Suppose that patients are randomly selected with replacement from the total for hospital 4 . What is the smallest sample size needed so that the probability is at least $90 \%$ that at least one patient is LWBS?

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Key Concepts

Minimum Sample Size Determination

Determining the smallest sample size needed to achieve a desired probability of witnessing at least one occurrence of an event involves setting up an inequality using the complement rule. This involves solving an exponential inequality where the probability that the event never occurs in all trials is set to be less than or equal to the complement of the desired probability. This approach is fundamental in designing experiments and studies to ensure sufficient power.

Random Sampling with Replacement

This concept refers to the method of selecting items from a population where each item is returned back to the population after its selection. This ensures that every selection is made from the same population distribution and that the trials are identical and independent, which is crucial for modeling probabilities in repeated experiments.

Complement Rule in Probability

The complement rule is the principle that the probability of at least one occurrence of an event is equal to one minus the probability that the event does not occur at all. This is especially useful when calculating probabilities for events over multiple independent trials, as it is often easier to compute the complement (no occurrences) than to sum the probabilities of one or more occurrences.

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