1 The Recording Industry Association of America provides dat

1) The Recording Industry Association of America provides data on the best-selling albums of all times. As of January, 2008, the top six best-selling albums of all times (U.S. sales only), are by the artists the Eagles (E), Michael Jackson (M), Pink Floyd (P), Led Zepplin (L), AC/DC (A), and billy Joel (B).

a. list the 15 possible samples without replacement of two artisis that can be selected from the six. For brevity, use the intial 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?

Solution

Sampling :

Defination : Its collection of subset from a set of items.Each observation measures one or more atrributes required to check from the subset items.

Sampling without Replacement :

Defination : When a unit is selected at random from the given set and is not returned into the main set ofitems is called samplng without replacaement.

For example : First item S₁ is selected at random from a population size N , Then second sample S₂ is drawn from the population size (N-1) .The sample without replacement is selected at random either by using permutations or combinations.

a) Answer for question :

The list of 15 simple random samples are given as   

6! / ( 6-2 )! * 2! = 15 samples,

given

A - AC/DC , B - Billy Joel , L - Led Zepplin , M - Mickel Jackson , P - Pink floyd , E - Eagles

b ) Selecting Simple Random Sample of 2 from 6.

The Sampling process has 7 Steps :

Simple Random Sample ( SRS ) : The simplest type of selecting a random sample, every item in the set has equal chances to be selected from the set.All items have same attributes in the set. Selecting sample 2 from a set of 6.

6!/(2! *4 !)

N _{C r} = N ! / ( r ! * (N-r) ! )

Combination of set N we need to draw a sample of r items.

c ) Simple random Sample : In this type of sample,All items have equal chances to get selected, from the above list of samples given in answer a). The chance for selecting P and A is 1 / 15^{th .} As total sample consists of 15 items and selecting that particular combination is 1/ 15 Chance. The same rule for selecting M and E is same as selecting P and A.