Mastering One-Sample Z-Interval For Population Proportion: A Comprehensive Guide

One Sample Z-Interval for Population Proportion CONDITIONS

1. Random sample or assignment2. 10% Condition n ≤ 1/10(N)3. p̂(n) ≥ 10 and (1-p̂)(n) ≥ 10

To construct a one-sample z-interval for a population proportion, you must ensure that the following conditions are met:

1. Random Sample: The data collected must be a random sample from the population of interest. This means that every member of the population has an equal chance of being included in the sample.

2. Independent Sample: The sample observations must be independent of each other. In other words, the response of one individual should not affect the response of another individual.

3. Large Sample: The sample size should be large enough to justify the use of a normal distribution. A general rule of thumb is that the sample size should be at least 10 times larger than the number of success and 10 times larger than the number of failures.

4. Success-Failure Condition: The number of successes and failures in the sample should be at least 10. This is known as the success-failure condition.

If these conditions are met, a one-sample z-interval for population proportion can be constructed using the following formula:

p̂ ± z* (√(p̂(1 – p̂)) / n)

Where,
p̂ is the sample proportion,
z* is the critical value of the standard normal distribution that corresponds to the desired level of confidence,
n is the sample size.

Note: p̂(1 – p̂) is the variance of the sample proportion. This formula assumes that the population proportion is unknown. If the population proportion is known, the formula changes slightly to replace p̂ with the population proportion p.

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