Question
How many different simple random samples of size 4 can be obtained from a population whose size is 47 ?
The number of simple random samples which can be obtained is
(Type a whole number.)
The number of simple random samples which can be obtained is
(Type a whole number.)
Ask by Romero Martin. in the United States
Mar 26,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
There are 178,365 different simple random samples of size 4 that can be obtained from a population of 47.
Solution
The number of different simple random samples of size 4 from a population of 47 is given by the combination formula
Step 1: Compute the numerator:
Step 2: Compute the denominator:
Step 3: Divide the numerator by the denominator:
Thus, the number of different simple random samples is
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Simplify this solution Mind Expander
To find the number of different simple random samples of size 4 from a population of size 47, you can use the combination formula, which is given by
Calculating this:
So, the number of different simple random samples of size 4 from a population of size 47 is 123,410.
Now, let’s dig a little deeper into the world of sampling!
Sampling strategies have been pivotal throughout history. Consider the 1936 US presidential election when The Literary Digest inaccurately predicted a victory for Alf Landon over Franklin D. Roosevelt based on a flawed sampling method. This event highlighted the critical importance of proper sampling techniques and set the stage for more rigorous statistical methods that followed.
In real-world applications, sampling is central to fields such as market research, healthcare, and social sciences. For instance, when launching a new product, companies might survey a diverse sample of potential customers to assess reaction before a full launch. This method helps them gather valuable insights while minimizing costs and time.
