### Description

**QUESTION **

- The following data were drawn from the Mexican Migration Project, a collaborative research effort based at Princeton University and the University of Guadalajara, supported by the National Institute of Child Health and Human Development (NICHD) and the William and Flora Hewlett Foundation (http://mmp.opr.princeton.edu/).

The variable of interest is the duration (in months) of stay in the United States during respondents’ final migration to the United States. A random sample of 5 respondents was drawn among those who spent between one and two years in the United States during their final migration. This process was repeated 25 times. The results are presented in file.

1.Suppose that instead of 25 random samples of size five, an infinite number of samples of size five were drawn. What would we call this?

2.If the population mean is 16 months, what is the expected mean of the sampling distribution? How do you know this?

3.Calculate the mean of the sample means.

4.Compare your result above to the mean of the sample means for only the first 10 samples. What differences do you notice and how might you explain them?

**QUESTION**

If you drew all possible random samples of size 100 from the population of LSAT test takers and plotted the values of the mean from each sample, the resulting distribution would be the sampling distribution of the mean. What is the value of the mean of the sampling distribution?

**QUESTION**

Calculate the value of the standard error of the mean for the sampling distribution for 100 samples.

**QUESTION**

1. A small population of N = 12 has values of 2, 2, 3, 4, 4, 7, 8, 8, 8, 9, 12, 12. Use this population to do the following:

a. Calculate the population mean:

b. Calculate the standard deviation for the population:

c. Draw three random samples of n = 3 from the population (use a simple random sampling procedure via randomizer.org). Remember to number your cases and select the corresponding cases from the original data set. List the selected corresponding values for each sample below:

Random sample #1:

Random sample #2:

Random sample #3:

d. Calculate the mean and standard deviation for each of the samples:

Random sample #1: Mean = SD =

Random sample #2: Mean = SD =

Random sample #3: Mean = SD =

e. Calculate the sampling error for each of the samples:

Random sample #1:

Random sample #2:

Random sample #3:

f. Which of your random samples was the best approximation of the population mean?

g. Which of your random samples was the worst approximation of the population mean?

h. Calculate the mean of the sampling distribution:

i. Calculate the standard error of the mean:

j. What could we do to make it a better approximation of the population mean?