# Question: Suppose that a simple random sample is taken without replacement

Suppose that a simple random sample is taken without replacement from a finite population of size N.

a. Show mathematically that Equations (7.1) and (7.2) are identical for samples of size 1.

b. Explain in words why part (a) is true.

c. Without doing any computations, determine σ. x for samples of size N without replacement. Explain your reasoning.

d. Use Equation (7.1) to verify your answer in part (c).

a. Show mathematically that Equations (7.1) and (7.2) are identical for samples of size 1.

b. Explain in words why part (a) is true.

c. Without doing any computations, determine σ. x for samples of size N without replacement. Explain your reasoning.

d. Use Equation (7.1) to verify your answer in part (c).

## Answer to relevant Questions

In Example 7.5, we used the definition of the standard deviation of a variable (Definition 3.12 on page 130) to obtain the standard deviation of the heights of the five starting players on a men's basketball team and also ...Desert Samaritan Hospital in Mesa, Arizona, keeps records of emergency room traffic. Those records reveal that the times between arriving patients have a special type of reverse-J-shaped distribution called an exponential ...According to the central limit theorem, for a relatively large sample size, the variable x-bar is approximately normally distributed. a. What rule of thumb is used for deciding whether the sample size is relatively large? b. ...An air conditioning contractor is preparing to offer service contracts on the brand of compressor used in all of the units her company installs. Before she can work out the details, she must estimate how long those ...In Example 7.9 on page 294, we conducted a simulation to check the plausibility of the central limit theorem. The variable under consideration there is household size, and the population consists of all U.S. households. A ...Post your question