Question

Suppose you are looking at the population of 8,000 students that are freshman at UTEP. You want to determine on average how many hours a week they work each week. Let’s call that number ?. You decide to take a sample of 100 of them.

• 1) How many data points are there in this space?
• 2) How many ways can you choose your subest of 100 students? Is it greater or less than the answer above.
• 3) How do you calculate the “point estimate” of one of those subsets of 100 students?
• 4) How many actual subsets of 100 students do you have as a researcher?
• 5) What does the Central Limit Theorem say about all the possible point estimates that can occur from the possible 100-student subsets? Draw a graph.
• 6) What value is the center of that curve? Please label it on the graph above.

Let’s just say the standard deviation of those 8,000 students is 5.

• 1) What is the formula for standard deviation of a population the 8,000 students (please make sure the summation sign has a starting and ending number)? Can it ever be negative? In our example, what are the units of the standard deviation?
• 2) What does the Central Limit Theorem say about the standard deviation of the curve discussed in question 5) above?
• 3) What is the standard deviation in our example?
• 4) What is the probability that a randomly picked sample has a point estimate within .5 of
  the actual mean ??
• 5) What is the probability that a randomly picked sample has a point estimate within 1 of
  the actual mean ??
• 6) Do you know whether our point estimate is higher or lower than the mean?

Answer 1