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.
if we have a group of values...1st we find its average..ie..'mean'..then we calculate each value's difeerence from the mean..then we will square each 'difference value'.then we devide total of sqared value by n or n-1..that is what variance...
you are working for a bank.The bank manager wants to know the mean waiting time for all customers who visit this bank. she has asked you to estimate this mean by taking a sample . Briefly explain how you will conduct this study. assume the data set on waiting times for 10 customers who visit a bank. Then estimate the population mean. choose your own confidence level.
how can we find the expectation of any function of X?
Jennifer
I've been using this app for some time now. I'm taking a stats class in college in spring and I still have no idea what's going on. I'm also 55 yrs old. Is there another app for people like me?
Tamala
Serious
Hamza
yes I am. it's been decades since I've been in school.
Tamala
who are u
zaheer
is there a private chat we can do
Tamala
hello
how can I get PDF of solutions introduction mathematical statistics ( fourth education)
who can help me
a box contains a few red and a few blue balls.one ball is drawn randomly find the probability of getting a red ball if we know that there are 30 red and 40 blue balls in the box
the following data represent the number of pop up advertisement received by 10 families during the past month.calculate the mean number of advertisement received by each family during month.43,37,35,30,41,23,33,31,16,21