HW 04

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George Mason University *

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310

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Statistics

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Feb 20, 2024

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1

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HW 04 1. How does the variance of the sample mean compare to the variance of the population? a. It is smaller and therefore suggests that averages have less variation than individual observations. 2. What is the relationship between the standard deviation of the sample mean and the population standard deviation? a. s ⅇ ( x ) = σ √ n 3. For any sample size n , the sampling distribution of is normal if the population from which the sample is drawn is uniformly distributed. a. False 4. For any population X with expected value µ and standard deviation σ, the sampling distribution of x will be approximately normal if the sample size n is sufficiently small. As a general guideline, the normal distribution approximation is justified when n < 30. a. False 5. The standard deviation of x (standard error of the sample mean) equals the population standard deviation divided by the square root of the sample size, or, equivalently. a. True s ⅇ ( x ) = σ √ n
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