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You have three data sets with the same standard deviation, S = 4.298. Data Set 1 has
ten observations in it (n=10), Data Set 2 has twenty (n=20), and Data Set 3 has fifty
observations in it (n=50). For each of these calculate the standard error.


Data Set 1: __________ Data Set 2: ____________ Data Set 3: ____________

Respuesta :

Using the Central Limit Theorem, it is found that:

  • The standard error of Data Set 1 is 1.36.
  • The standard error of Data Set 2 is 0.96.
  • The standard error of Data Set 3 is 0.61.

The Central Limit Theorem states that for a sample of size n in a population with standard deviation [tex]\sigma[/tex], the standard error is given by:

[tex]s = \frac{\sigma}{\sqrt{n}}[/tex]

In this problem, the standard deviation is [tex]\sigma = 4.298[/tex]

Then, for Data Set 1, [tex]n = 10[/tex], and:

[tex]s = \frac{4.298}{\sqrt{10}} = 1.36[/tex]

For Data Set 2, [tex]n = 20[/tex], and:

[tex]s = \frac{4.298}{\sqrt{20}} = 0.96[/tex]

For Data Set 3, [tex]n = 50[/tex], and:

[tex]s = \frac{4.298}{\sqrt{50}} = 0.61[/tex]

A similar problem is given at https://brainly.com/question/24188986

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