1.State whether each of the following statements concerning the sample mean is true or false. If false, then explain what would make the statement true.

a. The value of the sample mean equals the population mean on average.

b. The value of the sample mean can vary from sample to sample.

c. There is more than a 5% probability of selecting a sample mean that is farther than 2 SEM from the population mean.

d. The sampling distribution of sample means is approximately normally distributed.

2. A population is normally distributed with a mean of 56 and a standard deviation of 12.

a. What is the mean of the sampling distribution (M) for this population?

b. If a sample of 36 participants is selected from this population, what is the standard error of the mean (M)?

c. Sketch the shape of this distribution with M 3 SEM.

3. A population is normally distributed with a mean of 30 and a standard deviation of 4.

a. What is the mean of the sampling distribution (M) for this population?

b. If a sample of 16 participants is selected from this population, what is the standard error of the mean (M)?

c. Sketch the shape of this distribution with M 3 SEM.

4. Classroom assessment: Sampling and the population. Ryan (2006) reported about the effectiveness of an assignment given to students during a statistics class. The in-class assignment was aimed at helping students understand sampling distributions. In this study, participants selected 120 samples of size 3 from a population of 5 scores (0, 0, 0, 3, and 6) using the theoretical sampling strategy.

a.How many possible samples can be drawn from this population?

b. What is the population mean?

c. What is the population standard deviation?