# Study Questions

### Chapter 7

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 below.

 Sample Ÿ Sample Ÿ Sample Ÿ Sample Ÿ Sample Ÿ 1 18.65 6 16.87 11 19.30 16 15.42 21 15.00 2 17.76 7 17.57 12 17.63 17 12.59 22 15.34 3 18.38 8 17.98 13 19.54 18 17.23 23 10.58 4 18.02 9 13.55 14 14.00 19 15.38 24 16.71 5 14.37 10 15.15 15 14.66 20 15.54 25 19.40
1. Suppose that instead of 25 random samples of size five, an infinite number of samples of size five were drawn. What is the term for this distribution as it was introduced in Chapter 7?

2. Without doing any calculations, if the population mean is 16 months, what is the expected mean of the sampling distribution?

3. On what basis did you formulate your answer to Question #2? Discuss which theorem talks about the relationship between the population mean and the mean of the sampling distribution.

4. Calculate the mean of the sample means as they are displayed in the table at the opening of this question set.

5. 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 in terms of the material presented in Chapter 7?

6. Explain why your answer to Question #4 is not exactly 16.

7. Suppose we drew 15 more samples. Compared to your answer in Question #4, what would you expect the value of the mean of all 40 samples to be? Would be less than or greater than the value you calculated in Question #4?

8. Below are presented 15 additional sample means for samples of size 5. Considering these, calculate the mean for all 40 samples. Do these results confirm your answer in Question #7? Why or why not?
 Sample Ÿ Sample Ÿ Sample Ÿ 26 16.16 31 17.97 36 18.02 27 20.01 32 18.06 37 16.86 28 13.82 33 14.81 38 13.31 29 17.55 34 13.11 39 19.20 30 15.94 35 13.84 40 14.60