Determine whether the following statement is true or false. Explain the reason if the answer is false.

1. Because is an unbiased estimator of , =.

2. A sample average is computed in the same manner as a population mean.

3. A sample variance is computed in the same manner as a population variance.

4. If a population has a mean of 10 and a standard deviation of 2, then the sampling distribution of averages of samples of size n=2 has a mean of 10 and a standard deviation of 1. 5. The variance of a sampling distribution of averages is larger than the variance of the underlying population because has more distinct values than y.

6. Chebyshev's theorem shows that in all samples most of the data lie within three standard deviations of the average.

7. One of the advantages of using a sample average instead of a single observation to estimate the population mean is that the sample average is more likely to be close to the population mean.

8. The empirical rule cannot be applied to skewed distributions.

9. If the sampling is with replacement, the expected value of the sampling distribution of averages is different from the expected value when the sampling is without replacement.

10. A public opinion poll in which no person can be interviewed more than once is an example of sampling without replacement.