1 . Consider the box with 5 tickets marked 1, 2, 3, 4, 5. ( N=5 ). Take a simple

Question

1. Consider the box with 5 tickets marked 1, 2, 3, 4, 5. (N=5). Take a simple random sample of size 2 from this box. How many such samples are there? Remember, an SRS is like dealing a hand of cards from a deck. In this case, your deck has 5 cards and your hand has 2. How many such hands are there?

(a) List all the possible samples of size 2. For each of these samples, list its average. This is the sample mean for each sample.

(b) Write out all the possible values that the sample mean can take, along with the probability that it takes this value That is, create the probability distribution table for the sample mean of samples of size 2.

(c) Compute the expected value and the variance of the sample mean using the distribution table from (b). Use the probability distribution. Once you have the variance, then take its square root to compute SE of the sample mean. Find SE by computing the variance, and taking its square root.  

Explanation / Answer

Taking a sample of 2 tickets from a box of 5 tickets can be done in 5C2 = 10 ways.

(a)

Sample Average

1,2 1.5

1,3 2   

1,4 2.5   

1,5 3

2,3 2.5

2,4 3

2,5 3.5

3,4 3.5

3,5 4

4,5 4.5

(b) All possible mean values are {1.5, 2 , 2.5 , 3 , 3.5 , 4 , 4.5}

Sample mean Probability

1.5 1/10

2 1/10

2.5 2/10

3 2/10

3.5 2/10

4 1/10

4.5 1/10

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