Exam 6: Sampling Distributions

Which of the following describes what the property of minimum variance means?

The term statistic refers to a population quantity, and the term parameter refers to a sample quantity.

Consider the population described by the probability distribution below. x 2 5 7 p(x) .2 .5 .3 The random variable $x$ is observed twice. The observations are independent. The different samples of size 2 and their probabilities are shown below. Sample Probability 2,2 .04 2,5 .10 2,7 .06 Sample Probability 5,2 .10 5,5 .25 5,7 .15 Sample Probability 7,2 .06 7,5 .15 7,7 .09 Find the sampling distribution of the sample mean $\bar { x }$ .

The standard error of the sampling distribution of the sample mean is equal to σ, the standard deviation of the population.

Suppose students' ages follow a skewed right distribution with a mean of 21 years old and a standard deviation of 2 years. If we randomly sample 450 students, which of the following statements about the sampling distribution of the sample mean age is incorrect?

Consider the population described by the probability distribution below. x 3 5 7 p(x) .1 .7 .2 a. Find $\mu$ . b. Find the sampling distribution of the sample mean $\bar { x }$ for a random sample of $n = 2$ measurements from the distribution. c. Show that $\bar { x }$ is an unbiased estimator of $\mu$ .

Suppose a random sample of n = 36 measurements is selected from a population with mean μ = 256 and variance $\sigma ^ { 2 } = 144 \text {. Find the mean and standard deviation of the sampling distribution of the sample mean } \bar { x }$