Question

ch 15 the following are examples of statistics except
x - bar.
sigma.
s - squared.
s.
question 20
ch 15 the average age of residents in a large residential retirement community is 69 years with standard deviation 5.8 years. a simple random sample of 100 residents is to be selected, and the sample mean age $\bar{x}$ of these residents is to be computed. we know the random variable $\bar{x}$ has approximately a normal distribution because of
the 68 - 95 - 99.7 rule.
the central limit theorem.
the law of large numbers.
the population from which were sampling has a normal distribution.

Explanation:

1. In statistics, $\bar{X}$ (X - bar) is the sample mean, $S^{2}$ (S - squared) is the sample variance, and $S$ is the sample standard - deviation. These are all statistics. $\sigma$ (Sigma) represents the population standard deviation, which is a parameter, not a statistic.
2. The central limit theorem states that if you have a population with mean $\mu$ and standard deviation $\sigma$ and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed, regardless of the shape of the population distribution. Here, a sample of size $n = 100$ is large enough (usually $n\geq30$ is considered large), so the sample - mean $\bar{x}$ has approximately a normal distribution because of the central limit theorem. The 68 - 95 - 99.7 rule applies to a normal distribution but does not explain why the sample mean is normal. The law of large numbers is about the convergence of the sample mean to the population mean as the sample size increases. And we are not given that the population has a normal distribution.

Answer:

1. The answer to the first question is: B. Sigma
2. The answer to the second question is: the central limit theorem.