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Ch. 1 - Introduction to Statistics
Larson - Elementary Statistics: Picturing the World 8th Edition
Larson8th EditionElementary Statistics: Picturing the WorldISBN: 9780137493470Not the one you use?Change textbook
All textbooksLarson 8th EditionCh. 1 - Introduction to StatisticsProblem 1.3.22
Chapter 1, Problem 1.3.22

Volunteers for an experiment are numbered from 1 to 90. The volunteers are to be randomly assigned to two different treatment groups. Use a random number generator different from the one you used in Exercise 21 to choose 45 subjects for the treatment group. The other 45 subjects will go into the control group. List the subjects, according to number, in each group. Tell which method you used to generate the random numbers.

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Step 1: Understand the problem. You need to randomly assign 90 volunteers into two groups: a treatment group and a control group, each containing 45 subjects. This requires generating random numbers to ensure unbiased selection.
Step 2: Choose a random number generation method. For example, you can use a random number generator from statistical software (e.g., R, Python, Excel) or a physical method like drawing numbers from a hat. Specify the method you will use.
Step 3: Generate 45 unique random numbers between 1 and 90 using the chosen method. Ensure that each number corresponds to a volunteer and that no number is repeated. For example, in Python, you can use the function `random.sample(range(1, 91), 45)`.
Step 4: Assign the 45 selected numbers to the treatment group. The remaining 45 numbers (those not selected) will automatically be assigned to the control group.
Step 5: List the numbers in each group. Clearly document the numbers in the treatment group and the control group, and specify the random number generation method used (e.g., 'Python random.sample function').

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Random Assignment

Random assignment is a technique used in experiments to ensure that each participant has an equal chance of being assigned to any group. This process helps eliminate bias and ensures that the treatment and control groups are comparable, which is crucial for the validity of the experiment's results.
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Random Number Generation

Random number generation is the process of creating a sequence of numbers that cannot be reasonably predicted. In the context of this experiment, a random number generator is used to select participants for the treatment group, ensuring that the selection process is unbiased and truly random.
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Control Group

A control group is a baseline group in an experiment that does not receive the treatment being tested. This group is essential for comparison, as it allows researchers to determine the effect of the treatment by contrasting outcomes between the treatment and control groups.
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