Question 1192336: A manufacturer wishes to estimate the proportion of washing machines leaving the factory that is defective. How large a sample should she check in order to be 94 percent confident that the true proportion is estimated to within 0.015?
Answer by CPhill(1987)   (Show Source):
You can put this solution on YOUR website! **1. Determine the z-score:**
* Find the z-score that corresponds to a 94% confidence level. This means we want to find the z-score that leaves 3% in each tail of the standard normal distribution.
* Using a standard normal distribution table or calculator, we find that z ≈ 1.8808.
**2. Estimate the proportion of defective washing machines:**
* Since we don't have any prior information about the proportion of defective washing machines, we'll use the most conservative estimate: p = 0.5. This will give us the largest sample size needed.
**3. Calculate the sample size:**
* Use the following formula for determining the sample size needed for estimating a population proportion:
n = (z² * p * (1 - p)) / E²
where:
* n is the sample size
* z is the z-score
* p is the estimated proportion of defective washing machines
* E is the desired margin of error (0.015 in this case)
* Plug in the values:
n = (1.8808² * 0.5 * (1 - 0.5)) / 0.015²
n ≈ 7861.16
* **Round up:** Since we can't have a fraction of a washing machine, we round up to the nearest whole number.
**Therefore, the manufacturer should check a sample of 7862 washing machines to be 94% confident that the true proportion of defective washing machines is estimated to within 0.015.**
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