Q 1.45. - Elementary Statistics

Question

Best-Selling Albums. Refer to Exercise 1.44. 

(a). List the 15 possible samples (without replacement) of four artists that can be selected from the six. 

(b). Describe a procedure for taking a simple random sample of four artists from the six. 

(c). If a simple random sampling procedure is used to obtain four artists, what are the chances of selecting E, A, L, and B? P, B, M, and A?

Step-by-Step Solution

Answer

Part (a)  (E, M, P, L), (E, M, P, A), (E, M, P, B), (E, M, L, A), (E, M, L, B), (E, M, A, B), (E, P, L, A), (E, P, L, B), (E, P, A, B), (E, L, A, B), (M, P, L, A), (M, P, L, B), (M, P, A, B), (M, L, A, B), (P, L, A, B)

Part (b)  By writing all letters on separate pieces of paper to produce a simple random sample of size 4 we can select four artists from the six.

Part (c) $\frac{1}{15}$

Part (a) Step 1. Given information.

The given information is:

The Recording Industry Association of America provides data on the best-selling albums of all time. As of May 28, 2013, the top six best-selling albums of all time (U.S. sales only), are by the artists the Eagles (E), Michael Jackson (M), Pink Floyd (P), Led Zeppelin (L), AC/DC (A), and Billy Joel (B).

Part (a) Step 2. List the 15 possible samples of four artists that can be selected from the six.

The 15 possible samples (without replacement) of four artists that can be selected from the six best-selling albums of all time:

(E, M, P, L), (E, M, P, A), (E, M, P, B), (E, M, L, A), (E, M, L, B), (E, M, A, B), (E, P, L, A), (E, P, L, B), (E, P, A, B), (E, L, A, B), (M, P, L, A), (M, P, L, B), (M, P, A, B), (M, L, A, B), (P, L, A, B)

Part (b) Step 1. Describe a method for choosing four artists from a group of six using simple random sampling.

Procedure:

We might write the letters that correspond to the best-selling albums of all time (E, M, P, L, A, B) on separate pieces of paper to produce a simple random sample of size 4. 

Now we could pick four slips of paper while blindfolded after placing these six slips of paper in a box and shaking it.

Part (c) Step 1. If a simple random sampling procedure is used to obtain two artists, what are the chances of selecting E, A, L, and B, and P, B, M, and A .

Total samples are 15.

There is only one outcome of selecting E, A, L, and B.

Therefore, the Chance of selecting E, A, L, and B:

$=\frac{1}{15}$

There is only one outcome of selecting P, B, M, and A.

Therefore, the Chance of selecting P, B, M, and A:

$=\frac{1}{15}$