Stat226 SI: Understanding of sampling methods, experiments, sampling distribution and CLT.

  1. For each of the scenarios, indicate what kind of sampling method is used.

Major league Baseball, responding to concerns about their “brand” decides to test players to see weather they are using performance-enhancing drugs. The officials propose several different sampling ideas to test their players. Listed below are several different ideas proposed for gathering a representative sample.

a)The players are asked to come forward to receive testing. All players who come forward are tested.

b)Using a list of all players the officials randomly select 50 players for testing.

c)Officials select 4 teams at random and a drug-testing crew show up unannounced to test all players on the team.

d)A small testing crew is sent to each team and each crew randomly selects 5 players for testing.

e)The coach of one team selects all the players in his team for testing.

  1. Fill the blanks

#1______- observes individuals and measures variables of interest, but does not attempt to influence responses.

#2______- deliberately imposes some treatment on individuals to observe their responses. Requires a random assignment.

  1. Suppose that in a company the retirement fund is invested in five corporate stocks with the following returns, and the company interested in what the average return will be from the five stocks.

Stock...... Return

A...... 7%

B...... 12%

C...... -3%

D...... 21%

E...... 3%

1)In this example, what is the population? What is the parameter? What is the numeric value of the parameter?

2)Now, we decide to take a random sample of three stocks. Assuming that the order is not important and sampling is done without replacement.

Write an example of a random sample in this case. Calculate the mean for your example.

3) We can think of your mean as an educated guess of what quantity?

4)Select you second sample and calculate the mean. Was this value the same from the first mean you calculated? Why?

5)Write down how we can obtain the sampling distribution.

Part 1: Fill in the blanks

If 1.______is large enough, the 2.______follows

a 3.______with center 4.______and standard

deviation 5.______.

T or F: If the population distribution is normal, the 1.______must be at least 30 to ensure that the 2.______follows a 3.______.