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Chapter 7: Problem 70

Consider a large population with \(p=.63\). Assuming \(n / N \leq .05\), find the mean and standard deviation of the sample proportion \(\hat{p}\) for a sample size of a. 100 b. 900

Short Answer

Expert verified
For the sample size of 100, the mean is 0.63 and the standard deviation is calculated using the provided formula. Similarly, for the sample size of 900, the mean is 0.63 and the standard deviation is obtained using the same formula.

Step by step solution

01

Calculate Mean for Sample Sizes 100 and 900

Since the mean of the sample proportion \(\hat{p}\) equals the population proportion \(p\), for sample sizes of 100 and 900, the means will be \(p=0.63\).
02

Calculate Standard Deviation for Sample size 100

To calculate the standard deviation for sample size 100, use the formula \(\sqrt{(p(1 - p)/n)}\). Substituting given values: \( \sqrt{(0.63(1 - 0.63)/100)}\). This will give the desired result.
03

Calculate Standard Deviation for Sample size 900

To calculate the standard deviation for sample size 900, use the same formula. Substituting the given values yields: \( \sqrt{(0.63(1 - 0.63)/900)}\). This will give the required value.

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