Raising the bar

Chapter 7. Sampling and Sampling Distribution

Unit 7.4. Questions for repetition

Ex. 1. Fill out the next table:

Table 7.1. Population and sample formulas.

Ex. 2. How would you satisfy the definition of the simple random sampling in case of measuring average income of city residents?
Ex. 3. Define a sampling distribution and illustrate it with a sampling distribution of a sample proportion.
Ex. 4. Stating all the necessary assumptions, derive the formulas for the mean and variance of the sample mean.
Ex. 5. Suppose we sample from a Bernoulli population. How do we figure out the approximate value of $latex p$? How can we be sure that the approximation is good?
Ex. 6. Define unbiasedness and prove that the sample variance is an unbiased estimator of the population variance.
Ex. 7. Find the mean and variance of the chi-square distribution.
Ex. 8. Find $latex V(s_X^2)$ and a confidence interval for $latex s_X^2$. What assumptions do you use?

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