In designing an experiment involving a treatment applied to 4 test subjects, researchers plan to use a simple random sample of 4 subjects selected from a pool of 31 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? (Type an integer or a simplified fraction.)
Question
In designing an experiment involving a treatment applied to 4 test subjects, researchers plan to use a simple random sample of 4 subjects selected from a pool of 31 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? (Type an integer or a simplified fraction.)
Solution
a.) The number of different simple random samples possible can be calculated using the combination formula, which is C(n, k) = n! / [k!(n-k)!], where n is the total number of subjects, k is the number of subjects in each sample, and "!" denotes factorial.
In this case, n = 31 (the total number of available subjects) and k = 4 (the number of subjects in each sample). So, the number of different simple random samples possible is C(31, 4) = 31! / [4!(31-4)!].
This simplifies to C(31, 4) = 31! / [4!27!] = (31302928) / (4321) = 27,405.
b.) The probability of each simple random sample in this case is 1 divided by the total number of possible samples. So, the probability is 1 / 27,405.
Similar Questions
An experiment involves 30 participants. From these, a group of 4 participants is to be tested under a special condition. How many groups of 4 participants are possible?
For a simple random sample of size two, all samples of size two have the same chance of being chosen. What would the likelihood be of choosing any one of these samples?Group of answer choices4 in 101 in 62 in 61 in 2
Assuming the experiment was balanced: the number of different treatments used in the experiment, and the number of subjects (separate observations) for each treatment wereGroup of answer choices5 subjects on each of 4 treatments5 subjects on each of five treatments6 subjects on each of 4 treatments6 subjects on each of 5 treatments30 subjects on each of 4 treatments
In a simple random sampleQuestion 3Select one:a.Every item has the same chance to be in the sample.b.Every item has a chance to be in the sample.c.Every kth item is selected to be in the sample.d.All of these.
You randomly choose a whole number from 1 to 4 and a letter from A to D. Find the number of possible outcomes in the sample space.The number of possible outcomes in the sample space is .Question 2List the possible outcomes.
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.