46: Central Limit Theorem Activity
( \newcommand{\kernel}{\mathrm{null}\,}\)
This is an activity to verify the Central Limit Theorem. Be sure to enter in your answers as decimals rather than fractions when necessary.
A population consists of the numbers Find the population mean μ. Do this by hand and show your work.
Assuming samples of size n=2 are drawn with replacement between each selection. Let ˉx represent the mean of each of these samples. Find μˉx, the mean of the sample means. First, complete the table of means. The first row has been completed for you.
ˉx | p(ˉx) | ˉxp(ˉx) |
Now add all of the entries of the last column to arrive at μˉx.
μˉx=
x | x−μ | (x−μ)2 | |
Now, add up the last column:
∑4i=1(x−μ)2=
Now, find σx using the formula √∑Ni=1(xi−μ)2N Round your answer to four decimal places.
σx=
ˉx | ˉx2 | p(ˉx) | ˉx2p(ˉx) |
Now, add up the last column:
∑ˉx2p(ˉx2)=
Now, find σˉx using the formula √∑ni=1[¯xi2p(¯xi)]−μ2 Round your answer to four decimal places.
σˉx=
Next decide how σˉx compares to σ.
Now, find σx√n. Round your answer to four decimal places.
σx√n=