Essential Conditions For A Reliable One Sample Z-Test For Proportion In Statistics

One Sample Z-Test for Proportion CONDITIONS

1. Random sample or assignment2. 10% Condition n ≤ 1/10(N)3. a) Population distribution is stated as NORMAL b) n ≥ 30 c) if n < 30, check graph of sample data to verify no strong skew or outliers

The one sample z-test for proportion is a statistical hypothesis test that is used to compare a proportion in a sample to a known proportion in the population. This test determines the statistical significance of the difference between the sample proportion and the population proportion. However, before performing this test, it is important to ensure that certain conditions are met to ensure that the test results are reliable and valid.

The conditions that must be met before performing a one sample z-test for proportion are:

1. Independence: The sample observations must be independent of each other. This means that the selection of one individual should not influence the selection of another individual.

2. Sample size: The sample size should be large enough to ensure that the distribution of sample proportions is approximately normal. The rule of thumb is that for the one sample z-test, the sample size should be n ≥ 30.

3. Random sample: The sample should be selected randomly from the population. This ensures that the sample is representative of the population.

4. Success-failure condition: The number of successes and failures in the sample should be at least 10. This implies that the sample proportion and 1 minus the sample proportion should both be greater than or equal to 10%.

If these conditions are not met, the results of the test could be biased or inaccurate, and the test may not be appropriate for the data. Therefore, it is important to check these conditions before conducting a one sample z-test for proportion.

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