4.6 8)In designing an experiment involving a treatment applied to 6 test subject

Question

4.6

8)In designing an experiment involving a treatment applied to 6 test subjects, researchers plan to use a simple random sample of 6 subjects selected from a pool of 49 available subjects. (Recall that with a simple random sample, all samples of the same size have the same chance of being selected.) Answer the questions below.

a. How many different simple random samples are possible?

b. What is the probability of each simple random sample in this case?

9)When nine basketball players are about to have a free-throw competition, they often draw names out of a hat to randomly select the order in which they shoot. What is the probability that they shoot free throws in alphabetical order? Assume each player has a different name.

P(shoot free throws in alphabetical order)

(Please answer both questions and all parts)

Explanation / Answer

8) Here we have to draw a simple random sample of 6 subjects from 49 available subjects. Clearly this is a case of Simple Random Sample Without Replacement as we have to select different subjects.

Here N= 49 ( population size) and n=6(sample size)

a) Being SRSWOR, we can choose here NCn samples i.e 49C6 = 13983816 samples.

b) Here each subject is drawn with equal probability of 1/N= 1/49.

The probabilty of each random sample = 1/[N(N-1)(N-2)........(N-n+1)] = 1/[49*48*...*(49-6+1)]= 0.0993*10-9

9) There are 9 basketball players. So 9 players can be selected in 9! ways.

To choose their names in alphabetical order they have to selected in one order only( person with 1st letter comes first, person with second letter comes second, and so on)

So, P(Shoot free throws in alphabetical order) = 1/9! = 2.756*10-6

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