Answered

At IDNLearn.com, find answers to your most pressing questions from experts and enthusiasts alike. Discover in-depth answers from knowledgeable professionals, providing you with the information you need.

Doubling the size of the sample will a. double the standard error of the mean b. have no effect on the standard error of the mean c. reduce the standard error of the mean to approximately 70% of its current value d. reduce the standard error of the mean to one-half its current value

Sagot :

Using the Central Limit Theorem, it is found that the correct option regarding the standard error of the mean is given by:

c. reduce the standard error of the mean to approximately 70% of its current value.

What does the Central Limit Theorem states about the standard error of the mean?

By the Central Limit Theorem, the sampling distribution of sample means of size n has standard error [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

Doubling n, we have that:

[tex]s_d = \frac{\sigma}{\sqrt{2n}} = \frac{1}{\sqrt{2}}\left(\frac{\sigma}{\sqrt{n}}\right) = 0.7\left(\frac{\sigma}{\sqrt{n}}\right) = 0.7s[/tex]

Hence option C is correct.

More can be learned about the Central Limit Theorem at https://brainly.com/question/24663213

#SPJ1

Thank you for contributing to our discussion. Don't forget to check back for new answers. Keep asking, answering, and sharing useful information. IDNLearn.com has the solutions you’re looking for. Thanks for visiting, and see you next time for more reliable information.