Follow Up Questions

WISE Exercise 1

Questions, comments, difficulties? Please contact Dale Berger.

You may want to print this page and use it to record your answers.

1. As you increase the sample size (N), the dispersion of the sample means (i.e., the variance of the possible values of a sample mean):

1. becomes less.
2. becomes greater.
3. remains the same.
4. varies.
5. cannot be determined from the above information.

2. True or False? The standard deviation of a sampling distribution of means is smaller than the standard deviation of the population when the sample size is 2. Why?

3. Imagine you are working as a research consultant for a large organization. The organization is interested in examining employee satisfaction (essentially, how happy workers are with their jobs). The organization employs over 10,000 employees so having everyone complete the scale is not practical. The organization decides to take a random sample of employees and only administer the scale to these employees. The organization is assuming that the sample of employees will represent the attitudes of the entire population of employees. The organization is unsure as to how many people to administer the survey. One researcher at the organization wants to use a sample of 20 employees whereas the other researcher wants to use a sample of 100 employees. Which sample size should they choose? Why? Present statistical evidence for your answer.

4. Imagine we measured the height of all the male students at a particular college. We found that the average height of men at this school was 70 inches (5'10") with a standard deviation of 2 inches. If we were to randomly select one male student from this college, what is the probability that this student was 73 inches (6'1") or taller?

5. Still think about the same college in question 4. Imagine we selected 16 students at random. What is the probability that the average height of these 16 students is 73 inches or taller?

6. Imagine that you took a sample of students from the college in the prior questions and found a mean height of 68 inches. For which of the sample sizes below would you find this most surprising. (note: n = size of sample)

1. n = 10
2. n = 50
3. n = 100
4. n does not matter<

7. For problem 5 above, what is the population mean?

8. For problem 5 above, what is the sample mean?