The student will demonstrate and compare properties of the central limit theorem.
Given
X = length of time (in days) that a cookie recipe lasted at the Olmstead Homestead. (Assume that each of the different recipes makes the same quantity of cookies.)
Recipe #
X
Recipe #
X
Recipe #
X
Recipe #
X
1
1
16
2
31
3
46
2
2
5
17
2
32
4
47
2
3
2
18
4
33
5
48
11
4
5
19
6
34
6
49
5
5
6
20
1
35
6
50
5
6
1
21
6
36
1
51
4
7
2
22
5
37
1
52
6
8
6
23
2
38
2
53
5
9
5
24
5
39
1
54
1
10
2
25
1
40
6
55
1
11
5
26
6
41
1
56
2
12
1
27
4
42
6
57
4
13
1
28
1
43
2
58
3
14
3
29
6
44
6
59
6
15
2
30
2
45
2
60
5
Calculate the following:
μ
_{x} = _______
σ
_{x} = _______
Collect the data
Use a random number generator to randomly select four samples of size
n = 5 from the given population. Record your samples in
[link] . Then, for each sample, calculate the mean to the nearest tenth. Record them in the spaces provided. Record the sample means for the rest of the class.
Complete the table:
Sample 1
Sample 2
Sample 3
Sample 4
Sample means from other groups:
Means:
$\overline{x}$ = ____
$\overline{x}$ = ____
$\overline{x}$ = ____
$\overline{x}$ = ____
Calculate the following:
$\overline{x}$ = _______
s_{
$\overline{x}$ } = _______
Again, use a random number generator to randomly select four samples from the population. This time, make the samples of size
n = 10. Record the samples in
[link] . As before, for each sample, calculate the mean to the nearest tenth. Record them in the spaces provided. Record the sample means for the rest of the class.
Sample 1
Sample 2
Sample 3
Sample 4
Sample means from other groups
Means:
$\overline{x}$ = ____
$\overline{x}$ = ____
$\overline{x}$ = ____
$\overline{x}$ = ____
Calculate the following:
$\overline{x}$ = ______
s_{
$\overline{x}$ } = ______
For the original population, construct a histogram. Make intervals with a bar width of one day. Sketch the graph using a ruler and pencil. Scale the axes.
Draw a smooth curve through the tops of the bars of the histogram. Use one to two complete sentences to describe the general shape of the curve.
Repeat the procedure for
n = 5
For the sample of
n = 5 days averaged together, construct a histogram of the averages (your means together with the means of the other groups). Make intervals with bar widths of
$\frac{1}{2}$ a day. Sketch the graph using a ruler and pencil. Scale the axes.
Draw a smooth curve through the tops of the bars of the histogram. Use one to two complete sentences to describe the general shape of the curve.
Repeat the procedure for
n = 10
For the sample of
n = 10 days averaged together, construct a histogram of the averages (your means together with the means of the other groups). Make intervals with bar widths of
$\frac{1}{2}$ a day. Sketch the graph using a ruler and pencil. Scale the axes.
Draw a smooth curve through the tops of the bars of the histogram. Use one to two complete sentences to describe the general shape of the curve.
Discussion questions
Compare the three histograms you have made, the one for the population and the two for the sample means. In three to five sentences, describe the similarities and differences.
State the theoretical (according to the clt) distributions for the sample means.
n = 5:
$\overline{x}$ ~ _____(_____,_____)
n = 10:
$\overline{x}$ ~ _____(_____,_____)
Are the sample means for
n = 5 and
n = 10 “close” to the theoretical mean,
μ
_{x} ? Explain why or why not.
Which of the two distributions of sample means has the smaller standard deviation? Why?
As
n changed, why did the shape of the distribution of the data change? Use one to two complete sentences to explain what happened.
Questions & Answers
I only see partial conversation and what's the question here!
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest.
Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.?
How this robot is carried to required site of body cell.?
what will be the carrier material and how can be detected that correct delivery of drug is done
Rafiq
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
Source:
OpenStax, Introduction to statistics i - stat 213 - university of calgary - ver2015revb. OpenStax CNX. Oct 21, 2015 Download for free at http://legacy.cnx.org/content/col11874/1.3
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