The student will demonstrate and compare properties of the Central Limit Theorem.
Given:
= 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 #
Recipe #
Recipe #
Recipe #
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:
Collect the data
Use a random number generator to randomly select 4 samples of size
from the given
population. Record your samples below. Then, for each sample, calculate the mean to the nearesttenth. 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:
Calculate the following:
Again, use a random number generator to randomly select 4 samples from the population. This time, make the samples of size
. Record the samples below. 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:
Calculate the following:
For the original population, construct a histogram. Make intervals with bar width = 1 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 1 – 2 complete
sentences to describe the general shape of the curve.
Repeat the procedure for n=5
For the sample of
averaged together, construct a histogram of the averages (your means together with the means of the other groups). Make
intervals with
. 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 1 – 2 complete
sentences to describe the general shape of the curve.
Repeat the procedure for n=10
For the sample of
averaged together, construct a histogram of the averages (your means together with the means of the other groups). Make
intervals with
. 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 1 – 2 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.
:
~
:
~
Are the sample means for
and
“close” to the theoretical mean,
?
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 1 – 2 complete
sentences to explain what happened.
This lab was designed and contributed by Carol Olmstead.
Questions & Answers
differentiate between demand and supply
giving examples
In economics, a perfect market refers to a theoretical construct where all participants have perfect information, goods are homogenous, there are no barriers to entry or exit, and prices are determined solely by supply and demand. It's an idealized model used for analysis,
When MP₁ becomes negative, TP start to decline.
Extuples Suppose that the short-run production function of certain cut-flower firm is given by: Q=4KL-0.6K2 - 0.112 •
Where is quantity of cut flower produced, I is labour input and K is fixed capital input (K-5). Determine the average product of lab
Kelo
Extuples Suppose that the short-run production function of certain cut-flower firm is given by: Q=4KL-0.6K2 - 0.112 •
Where is quantity of cut flower produced, I is labour input and K is fixed capital input (K-5). Determine the average product of labour (APL) and marginal product of labour (MPL)
Quantity demanded refers to the specific amount of a good or service that consumers are willing and able to purchase at a give price and within a specific time period. Demand, on the other hand, is a broader concept that encompasses the entire relationship between price and quantity demanded
Ezea
ok
Shukri
how do you save a country economic situation when it's falling apart
Economic growth as an increase in the production and consumption of goods and services within an economy.but
Economic development as a broader concept that encompasses not only economic growth but also social & human well being.
Shukri
production function means
Jabir
What do you think is more important to focus on when considering inequality ?
sir...I just want to ask one question... Define the term contract curve? if you are free please help me to find this answer 🙏
Asui
it is a curve that we get after connecting the pareto optimal combinations of two consumers after their mutually beneficial trade offs
Awais
thank you so much 👍 sir
Asui
In economics, the contract curve refers to the set of points in an Edgeworth box diagram where both parties involved in a trade cannot be made better off without making one of them worse off. It represents the Pareto efficient allocations of goods between two individuals or entities, where neither p
Cornelius
In economics, the contract curve refers to the set of points in an Edgeworth box diagram where both parties involved in a trade cannot be made better off without making one of them worse off. It represents the Pareto efficient allocations of goods between two individuals or entities,
Cornelius
Suppose a consumer consuming two commodities X and Y has
The following utility function u=X0.4 Y0.6. If the price of the X and Y are 2 and 3 respectively and income Constraint is birr 50.
A,Calculate quantities of x and y which maximize utility.
B,Calculate value of Lagrange multiplier.
C,Calculate quantities of X and Y consumed with a given price.
D,alculate optimum level of output .
the market for lemon has 10 potential consumers, each having an individual demand curve p=101-10Qi, where p is price in dollar's per cup and Qi is the number of cups demanded per week by the i th consumer.Find the market demand curve using algebra. Draw an individual demand curve and the market dema
suppose the production function is given by ( L, K)=L¼K¾.assuming capital is fixed find APL and MPL. consider the following short run production function:Q=6L²-0.4L³ a) find the value of L that maximizes output b)find the value of L that maximizes marginal product