A population of N =100,000 people have an average annual income of m=$30,000 (with s=$1,000). Assume that I do not know the population mean and want to estimate it by taking a sample of people from the population.

a. Can I expect the average income of a sample of n =100 people to be equal to the average income of all of those people (N=100,000)? Why or why not? If you said no, what is the difference between the population mean and the sample mean called?

b. What is a sampling distribution? What is the distribution of sample means? How would I create such a distribution for the above example?

1. If I did create such a distribution, what would be the value of its mean? What shape would it have? What would happen to its shape if I increased the sample size to n = 200?

2. Calculate the standard deviation of this fictitious distribution of sample means (assume n = 100). What is the real name of this standard deviation?

Page Break3. What is the probability of obtaining a random sample of n=100 that has a mean of $30,000 or more from this distribution? What is the probability of obtaining a random sample of n=100 that has a mean of $29,900 or more from this distribution?

4. I take a sample of n =100 people from this distribution and I put them through a financial seminar. Six months later, they are making an average of $30,200 a year. Did the seminar produce a statistically significant increase in their income? (HINT: you can use a z-score hypothesis test for this problem)

5. I want to find out if men make more than women, so I take a sample of n =100 men and n =100 women. I find that men make an average of $30,100 and women make an average of $29,800. Assume the pooled variance is 500,000. Do men make significantly more than women? Use = .05. (HINT: use an independent-measures t test for this problem).