I will be positing screen shots of everything that is needed to complete this assignment ..this assignment needs to be completed by 6:00 pm on Sunday 11/24/2019 all screen shots are attached to this question

^{Hello I need the 2 test taken for macroeconomics Econ test 1 and 2. but the test are Proctorio and want to make sure that the test can be taken by tomm 12:00 pm noon.}

Lab homework using r instructions below

LAB HOMEWORK INSTRUCTIONS

——————————————————————-

#save your plots as an image file and upload separately (export > save as image)

#save them as png with filename your_name_(question number)_(histogram/plot)

#You are told that in Providence Rhode Island the height of women averages 64 inches (5’4″) with a standard deviation of 1.5 inches.

#Of the 178 thousand people in Providence Rhode Island, 52% are women.

#PART 1

#1.1) Simulate the population described above. Call the population variable popri

#1.2) Compute the mean and sd of this population.

#How does this mean and sd compare to the true mean (64) and sd (1.5)?

#1.3) Plot a density plot of this population. What does this distribution look like?

#PART 2

#2.1) Take a random sample of popri containing 10 people and call the variable sam10

#2.2) Compute the mean and sd of the sample sam10

#2.3) Take a random sample of popri containing 1000 people and call the variable sam1000.

#2.4) Compute the mean and sd of the sample sam1000

#2.5) Which is closer to the true population mean and sd; the sample with 10 people or the sample with 1000 people? Why?

#PART 3

#3.1) Create a matrix called samsri containing 200 random samples of 500 subjects in each sample from the population variable popri.

#HINT: Declare an empty matrix and then use a ‘for loop’ to fill it

#3.2) Create a vector called samsri200means that contains the means for each column (sample) from samsri.

#3.3)Plot a density plot of samsri200means (0.5 pt). What does this distribution look like?

——————————————————————————————

HERE’S A LECTURE ON WHAT WE LEARNED IN CLASS FOR THE LAB HOMEWORK DOWN BELOW FOR YOUR REFERENCE

#Lab 4-Contents

#0. Review of Normal Probability Distribution Functions

#1. Simulating Populations using Random Variables

#2. Taking Samples from a Population: The sampling Distribution

#3. Programming in R: Using Loops

#4. Programming in R: The apply function

#5. Sampling Distribution of the Uniform Distribution

#——————————————————–

# 0. Review of Normal Probability Distribution Functions

#——————————————————–

#Last week we learned how to calculate:

#1) Probabilities from a Normal Distribution using pnorm(Z, mean, sd)

#Ex: What is the probability of a student getting a 75 or less on the exam

#2) Quantiles from a Normal Distribution using qnorm(Z, mean, sd)

#Ex: What score would a student have to achieve to be in the top 10% on the exam

#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#

#EXERCISE 0-1: What is the probability of a student

#getting a 75 or less on the exam given that

#the scores on the exam follow a normal distribution

#of mean 78, and standard deviation of 10?

#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#

pnorm(75, 78, 10)

#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#

#EXERCISE 0-2: What score would a student have to achieve

#to be in the top 10% on the exam given

#the scores on the exam follow a normal distribution of mean 78,

#and standard deviation of 10?

#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#

qnorm(.9, 78, 10)

#——————————————————–

#1. Simulating Populations using Random Variables

#——————————————————–

#The difference between a population and a sample:

#Your sample is the group of individuals who participate

#in your study, and your population is the broader group

#of people to whom your results will apply.

#Therefore: “population” in statistics includes all members of a defined group.

#A part of the population is called a sample.

#^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

#Last week (Lab 3), we used the command rnorm()

#to create a variable with a normal distribution

#Random Normal variable: rnorm(n, mean, sd)

#NOTE: We can specify how large our population is,the mean and SD.

#^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#

#EXERCISE 1-1:

# Create a normally distributed population variable called pop

# that consists of 10,000 subjects with mean of 15 and sd of 2

#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#

#set.seed(1)

pop = rnorm(n=10000, mean=15, sd=2)

#Let’s verify that this did what we wanted.

hist(pop); mean(pop); sd(pop)

#??????????????????????????????????????????????????????????????????????????????????#

#Thought Question 1: Why is your mean and sd for pop slightly different

#than mine OR rather, why is noones exactly a mean of 15 and sd of 2

#??????????????????????????????????????????????????????????????????????????????????#

#??????????????????????????????????????????????????????????????????????????????????#

# Now, let’s pretend this variable x is a population of

# undergrads + graduate students at USC who have ever used marijuana

#Thought Question 2: Considering that USC is ~20k students,

#In reality, could I actually collect this information from every USC

#student to form this distribution? What should I do instead?

#??????????????????????????????????????????????????????????????????????????????????#

#—————————————————————

#2. Taking Samples from a Population: The sampling Distribution

#—————————————————————

#All (most) research studies deal with samples

#We can take a sample from data we consider to be our population

#by using the sample() function in R

#^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^#

#Random sample:sample(x, size, replace=TRUE)

#^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^#

#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#

#Example 1: Let’s pretend we are researchers.

#While ideally we would like to study the POPULATION of marijuana users

#at USC, we realize that we only have funding to ask 200 students.

#We can see what our data might look like if we take a sample from

#the population variable pop.

#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#

sam = sample(x=pop, size=200, replace=TRUE)

#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#

#Exercise 2-1: Calcualte the mean and SD of the sample sam.

#How do these results differ from the means

# and SDs in the pop variable?

#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#

mean(sam); sd(sam); hist(sam)

#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#

#Exercise 2-2:

# A) Create a random sample called sam20 from pop containing 20 subjects.

# B) Create a random sample called sam750 from pop containing 750 subjects.

# C) Compute the Means and SDs for sam20 and sam750. Create Histograms for both.

# D) How do the means from each sample compare to the true population mean of 15?

# E) Is there an association of the number of people in the sample with the magnitude of

# the difference from the populaton mean?

#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#

#A)

sam20=sample(pop, 20, replace=TRUE)

#B)

sam750=sample(pop, 750, replace=TRUE)

#C)

mean(sam20); mean(sam750)

sd(sam20); sd(sam750)

plot(density(sam20)); lines(density(sam750), col=”red”)

#D)

abs(15-mean(sam20)); abs(15-mean(sam750))

#E)

#As the number of people in the sample goes up,

#the mean becomes closer to the true population mean

#—————————————————————

#3. Programming in R: Using Loops

#—————————————————————

#In practice, as researchers we almost always have samples

#and NEVER really know the true population

#Simulating a population and taking samples from it can tell us something

#about how well a given estimator (mean, trimmed mean, median etc.)

#represents a distributions (eg. normal vs skewed)

#To begin to understand how taking samples can give us information about an estimator,

#we need to take MANY samples from our simulated population.

#Let’s say we wanted to have 100 different samples of pop with 200 subjects in each sample.

#We could do this two ways:

#1) Write the function sample() many times

sam1=sample(pop, 200, replace=TRUE)

sam2=sample(pop, 200, replace=TRUE)

# …

sam100=sample(pop, 200, replace=TRUE)

#2) Or use a loop

#^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^#

#Loop over ii: for (ii in X:Y) { # ii is the counter

#COMMANDS WITH ii # X is the first value the counter

#} # Y is the last value of the counter

#^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^#

# x=23+24;x

#print(x)

#Here is a simple loop going from a value of 1 to 10

for (jj in 1:10) {

print(jj)

} #NOTE: When executing the loop,

#you MUST highlight and run the entire loop from { to } including the brackets.

# ii will take the values specified with the “in 1:10” argument

#At first ii = 1, but then will increase by 1 (1,2,3,4,5…) until it reaches 10

#Also we can change ii to be whatever we want.

#Below I’ve used my name to demonstrate this

for (kk in 1:15) {

print(kk)

}

#Back to our goal:

#We want to be able to take 100 different samples of pop with 200 people in each sample

#A good way to do this is to first create an EMPTY matrix to put our data

#into using the matrix() command

mysams = matrix(, ncol=100, nrow=200) #? Why ncol=100 and nrow=200?

#Then we can use a loop to place each of our samples into a column of this empty matrix called “mysams”

for (ii in 1:100) {

mysams[ ,ii] = sample(pop, size=200, replace=TRUE)

}

#Look to your right and double click over ‘mysams’

#—————————————————————

#4. Programming in R: The apply function

#—————————————————————

# We just learned how to use a loop to take MANY random samples

# from a population variable. While the purpose of this

# may not be clear just yet, it will be later on in the semester.

#Once we have our dataset containing 100 samples of 200 people, I’d like to find out the mean of each sample

#I could do this two ways:

#1) By manually doing it

mean(mysams[,1])

mean(mysams[,2])

#…

mean(mysams[,100])

#2) By using a loop

for (jj in 1:100) {

print( mean(mysams[,jj]) ) #I have to use print() here because things in loops don’t get output to the screen without it

}

#However, I don’t just want to KNOW the means of each sample, instead I’d like to have a variable

#where each observation is the mean of a given sample so that I can analyse the means of the samples

#We can do this by first creating an empty Vector of length 100

sam100means = numeric(100)

#And then using a loop to populate the vector

for (jj in 1:100) {

sam100means[jj] = mean(mysams[,jj])

}

#With this, I can examine the average (mean) of the means for each sample

mean(sam100means)

#And their distribution

hist(sam100means)

#There is an easier way to get this sam100means variable,

#We can use the apply() function!

#^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^#

#Collapse Data (apply): apply(X, MARGIN, FUN)

# X=dataset; MARGIN: 1=Rows, 2=Columns; FUN=Function

#^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^#

#I will create a variable called sam100means2 containing the column means of mysams

sam100means2 = apply(X=mysams, MARGIN=2, FUN=mean)

#In the above: MARGIN=2 tells R to do the operation on the columns

#FUN=mean tells R to take the mean

#A Density plot of this:

plot(density(sam100means2))

#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#

#Exercise 4:

# A) Create a variable called sam100sd that contains the standard deviations of each

# sample from mysams. Use whatever method you prefer to do this.

# B) Show a density plot of the SDs from mysams

#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#

#A)

sam100sd = apply(X=mysams, MARGIN=2, FUN=sd)

#Alternately

sam100sd1=numeric(100)

for (i in 1:100) {

sam100sd1[i]=sd(mysams[, i])

}

#B)

plot(density(sam100sd))

#—————————————————————

#5. Sampling Distribution of the Uniform Distribution

#—————————————————————

#While we’ve seen that the distribution of means

#from random samples taken from a NORMAL population

#are normally distributed, what if our population is not normally distributed?

#Let’s see for example the uniform distribution

# which can be created using the runif() function

#^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^#

#Random Uniform variable: rnunif(n)

#^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^#

#I’ll create a uniform population distribution of 10,000 subjects

popunif = runif(10000) #Unifor distribution

#This distribution looks like:

hist(popunif)

#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#

#Exercise 5:

# A) Create a matrix called unifsams that contains 150 random samples of 250 subjects from popunif

# B) Create a variable called unif150means that contains the means for each of the 150 samples

# C) Create a density plot of means in unif150means. What does this plot look like?

#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#

#A)

unifsams = matrix(, ncol=150, nrow=250)

for (ii in 1:150) {

unifsams[,ii] = sample(popunif, 250, replace=TRUE)

}

#B)

unif150means = apply(unifsams, 2, mean)

#C)

plot(density(unif150means ))

#Normally Distributed remember the Central Limit Theorem.

# Read from the book section 5.3.2 to get a theoretical explanation about this last excercise

#Section:5.3.2 Approximating the Sampling Distribution of the Sample Mean: The General Case

Question 1

1. The opposite angles of a parallelogram are congruent.
   

   		TRUE
   		FALSE

2 points

Question 2

1. In a rectangle, the opposite sides are congruent.
   

   		TRUE
   		FALSE

2 points

Question 3

1. If a parallelogram is a rectangle then the diagonals are congruent.
   

   		TRUE
   		FALSE

2 points

Question 4

1. The following is a rhombus, therefore
   
   

   		TRUE
   		FALSE

2 points

Question 5

1. If a quadrilateral is a kite, then its diagonals bisect each other.
   

   		TRUE
   		FALSE

2 points

Question 6

1. ABCD is a parallelogram. If AE is equal to and EC is equal to b – 15, find the measure of AE.
   

   Question 7

   The diagonals of rhombus FGHJ intersect at point K. If side GK is equal to 3x – 5 and side JK is equal to 4x – 8, find x.

   Question 8

   A rectangle ABCD has the following sides. Find x and y.
   

   Question 9

   ABCD is a parallelogram. If angle B is equal to (2x)° and angle A is equal to (-x + 120)°, find x.
   

   Question 10

   ABCD is a parallelogram. If AB is equal to 2x + 1 and CD is equal to x + 13, find x.
   

   Question 11

   Triangle ABC and DEF are congruent. Find x.
   

   Question 12

   Triangle ABC is congruent to triangle DFE. Find x.
   

   Question 13

   Triangle RSV is congruent to triangle TVS. Find x and y.
   

   Question 14

   Triangle ABC is congruent to triangle DFE. Find x.
   

   Question 15

   Triangles QVS and RTS are similar. Find side VS.

   

   Question 16

   Triangles WSR and TVR are similar. Find x.
   

   Question 17

   Triangle ABE is similar to triangle ACD. Find y.
   

   Question 18

   Triangles MOP and MNQ are similar. Find x.
   

   Question 19

   Find x.
   

   Question 20

   Find x.
   

   Question 21

   Point C is the center of the circle. Angle ACB measures What is the measure of arc AB?
   

   Question 22

   Point C is the center of the circle. What is the measure of angle ACB if arc ADB measures ?
   

   Question 23

   Point C is the center of the circle. What is the measure of arc AB if ACB is equal to ?
   

   Question 24

   Point C is the center of the circle. What is the measure of arc ADB if ACB is equal to ?
   

   Question 25

   Angle C is an inscribed angle of circle P. Angle C measures and arc AB measures (-8x) . Find x.
   

   Question 26

   Point C is the center of the circle. If angle ACB measures
   and AB measures (x + 13) , find x.
   

   Question 27

   Circles M and K are congruent, is congruent to . Find the length of .
   

   Question 28

   Circles M and K are congruent, is congruent to and is congruent to
   . Find x and y.
   

   Question 29

   Circles M and K are congruent, is congruent to and is congruent to
   . Find x and y.
   

   Question 30

   Circles M and K are congruent, is congruent to and is congruent to
   . Find x and y.
   

   Question 31

   Find the if angle A is equal to and measures .
   

   Question 32

   and are tangent to circle D. Find x if = and = 7. Find x.

   Question 33

   and are tangent to circle D. Find x if = -x + 6 and = 3x + 1. Find x.
   

   Question 34

   Find x.
   

   Question 35

   Find angle A if is equal to and is equal to .
   
   

Descriptive Statistics Project:For this project you will be collecting data on some type of group difference and performing avariety of descriptive statistics using SPSS and the skills learned in class. First, you will need to collectdata on some type of group difference. For example, a group difference you might want to investigate isgender differences. In society there are many perceived gender differences. Some of these perceivedgender differences may exist and others may only be false stereotypes. If you want, you can use genderas one of your variables and then select a second variable you wish to investigate. Choose a variable thatis of interest to you such as academics, a hobby, or even a stereotype you believe may be inaccurate.If you are not interested in gender differences, there are many other groups that you couldinvestigate. For example, you could examine students in a Greek organization versus students not in aGreek organization. You could study students who live on-campus versus students who live off-campus,or even people who exercise daily versus people who do not exercise at all.First, select the two groups of people you want to study (eg., men & women). Then select avariable you wish to investigate (e.g., number of study hours per week a freshman studies). The morecreative you are, the better! Further, collect data that you might be able to utilize for future projects in thiscourse. (**Please note that RR#2 is an Independent Samples t-test. Therefore, we would hope thatyou could use your same data for RR#1 AND RR#2. Using Interval or Ratio data for a DependentVariable is necessary. Nominal or Categorical Data for your Dependent Variable would not beappropriate)!**Make sure that your dependent variable meets the Institutional Review Board’s (IRB)criteria. Pages 212-216 of the Homework Packet provides information on which variables andtopics are NOT exempt from receiving automatic institutional approval.Collect data from exactly 16 people in your first group, and exactly 16 people in yoursecond group. (So if you are investigating gender differences, for example, collect data from exactly 16females and 16 males). Ask each participant your question or get your measurement. Please try andkeep the subject responses confidential (you will be more likely to get honest and accurateanswers—this also protects the subject). Record your data in a table that includes the participants’group and their response.2**When completing this project, please watch for differences between the project guidelines, theversions of SPSS, and the instructions in the Homework Packet**Complete the following:1. Write an introduction explaining the following: (3 points)a) how and where you collected your datab) what you controlled for and could not control for as a researcher(That is, explain what other influences or independent variablesthat you could/did not control that may have resulted in your data set notaccurately representing your groups. [That is (for example), what kindsof factors can control how much sleep a person gets? Were thosefactors that you could control or did not have control over whilecollecting your data?]c) why you are studying these particular variablesd) what you expect to find, and WHY!e) **be sure to add a copy of your data**2. What is your independent variable? What is your dependent variable? For each variable identify thefollowing: a) type of data: categorical or measurement (2 points)b) scale of measurement: nominal, ordinal, interval, ratioc) Is the dependent variable discrete or continuous?3. Using SPSS, construct a frequency distribution for each group. Include output here. Discuss yourfindings [For example, what scores did most of your participants get; were the scores groupedtogether, or all spread out; etc…]. (1 point)4. Using SPSS, construct a histogram for each group. Include output here. Be sure the axes are clearlylabeled. Based on the graphs, describe the shape and modality of each distribution. (Hint: You willneed to split your file in SPSS) [For example, are your distributions normal? This could impacthow you answer question 5c] (1 point)5. Using SPSS calculate the mean, median, and mode for each group. Include your output. Based onyour findings, answer the following: (2 points)a) What is the average score in each distribution?b) What score corresponds to the 50th percentile in each distribution?c) Which measure of central tendency is the better one to report for each of yourdistributions and explain why?6. Using SPSS, calculate the range, variance, and standard deviation for each distribution. Include youroutput. (1 point)a) Interpret the standard deviation for each group.b) Do you have much variability in your data?c) Which distribution has more variability?7. Using SPSS create a z-distribution for each group. Include/provide your output. (3 points)a) What raw score best corresponds to the top 20% for each distribution?b) What raw score best corresponds to the 30th percentile for each distribution?(Hint: Look up the corresponding z-scores in your tables and find which values in each ofyour distributions best (is closest to) the z-score you looked up)[Using Howell, find the z-scores at the 30th percentile, and the top 20% or 80thpercentile. Now look at your z-distribution for each of your 2 groups and find the zscores that are closest….what are the corresponding raw scores?]8. Summarize your project. In your summary, make sure that you address all control factors that youdiscussed in your introduction. Further, provide insight on why you got the results that you did.(2 points)