If we want to draw a sample random sample from a population of 4000 items, how large a sample do we need to draw if we desire to estimate the percent defective within 2% of the true value with 95.45% probability.

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Answer 1

If we need to draw a sample of at least 2401. items from the population to estimate the percent defective within 2% of the true value with 95.45% probability.

What is a Random Sample?

A random sample is a subset of a population selected in such a way that each member of the population has an equal chance of being included in the sample.

To determine the required sample size for estimating the percent defective with the desired level of precision and probability, we can use the following formula:

n = (Z² * p * q) / E²

where:

n is the sample size

Z is the z-score corresponding to the desired level of confidence, which is 1.96 for 95.45%

p is the estimated proportion of defective items in the population

q = 1 - p is the proportion of non-defective items in the population

E is the desired margin of error, which is 0.02 (2% in decimal form)

Given that we don't have a prior estimate of the proportion of defective items in the population, we can use the conservative value of p = 0.5.

Therefore, q = 0.5 as well.

Substituting the values, we get:

n = (1.96² * 0.5 * 0.5) / 0.02²

n = 2401

Thus, the required sample size is 2401.

Therefore, we need to draw a sample of at least 2401 items from the population of 4000 to estimate the percent defective within 2% of the true value with a 95.45% probability.

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