Five bundles of pencils contain the quantities shown in the table: Bundles: A, B

Question

Five bundles of pencils contain the quantities shown in the table:

Bundles: A, B, C, D, E

Number of pencils: 10, 7, 10, 11,12

a. How many different samples of 3 bundles each are there?

b. List all possible samples of size 3 and compute the mean of each sample:

Set up a table like below for:

Sample #, Bundle #1, Bundle #2, Bundle #3, Total pencils, Mean number of pencils

c. Calculate the frequency and probability of each sample mean:

Set up a table below for:

Sample mean, Frequency, Probability

D. What observations can be made about the population and the sampling distribution?

Explanation / Answer

a) 5 bundles and we need to select 3 bundles out of it. So, 5C3 ways = 5C2 = 5*4/2 = 10 ways

b)

c)

d) Population mean and mean of the sample should turn out to be the same as we have taken all the exhaustive cases to form the samples.

Sample# Bundle #1 Bundle #2 Bundle #3 Total Pencils Mean 1 A B C 27 9 2 A B D 28 28/3 3 A B E 29 29/3 4 A D C 31 31/3 5 A E C 32 32/3 6 A D E 33 11 7 B C D 28 28/3 8 B C E 29 29/3 9 C D E 33 11 10 B D E 30 10

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