Q 1.44. - Elementary Statistics

Question

Best-Selling Albums. 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). 

(a). List the 15 possible samples (without replacement) of two artists that can be selected from the six. For brevity, use the initial provided. 

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

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

Step-by-Step Solution

Answer

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

Part (b)  By Using Random Table, a line number and column number can be chosen first at random, and then two numbers from 1 to 6 are chosen by moving down in the selected column. 

Part (c)  0.067.

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 two artists that can be selected from the six.

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

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

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

Procedure:

Using Random Table, two artists out of the given six can be chosen at random.

The artists are listed in order from 1 to 6. 

From the Random Table, a line number and column number are chosen at random, and two numbers from 1 to 6 are chosen by moving down in the selected column. 

As a result, two artists are chosen at random from a pool of six.

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

Total samples are 15.

There is only one outcome of selecting P and A.

Therefore, the Chance of selecting P and A:

$$\begin{gathered} =\frac{1}{15} \\ =0.067 \end{gathered}$$

Similarly, there is only one outcome of selecting M and E.

Therefore, the Chance of selecting M and E is:

$$\begin{gathered} =\frac{1}{15} \\ =0.067 \end{gathered}$$