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Explanation & Answer
As we know that
Cos (60 deg) = 4 / x
x = 4 / Cos (60 deg)
x = 4 / 0.5
x = 8
Hence Hypotenuse = 8
HOPE you get it. thanks :)
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Harvard Stats Homework Using R Lab 5 Help
stats homework using RHomework- lab 5:#The central limit theorem (CLT) states that as the sample size gets sufficiently la ...
Harvard Stats Homework Using R Lab 5 Help
stats homework using RHomework- lab 5:#The central limit theorem (CLT) states that as the sample size gets sufficiently large, the distribution of the sample means will be normally distributed.#In addition, the CLT has been used to justify the fact that for many of our statistics we rely upon computing the mean (not median or trimmed mean) of our samples#There are a few problems with the CLT. #1) How large of a sample is needed#2) It seems that our experiments with the contaminated normal may contradict this.#In this homework assignment you will investigate the CLT further. #PART 1 - The Central Limit Theorem under Normality.#1.1) Simulate a standard normal population of 1 million people called pop1 #1.2) Draw 5000 samples of size 20 and put these in sam20. Draw 5000 samples of size 50 and put these in sam50 .#1.3) Create variables called sam20means and sam50means that contains the means of the samples . Use a density plot to show the sampling distribution of the means for sam20means and sam50means together#1.4) Compare the Standard Error (SE) of the sampling distributions. Which sample size creates better estimates of the population mean (ie. has the lowest SE)? #PART 2 - The Central Limit Theorem under Non-Normality#2.1) Simulate a contaminated normal population using cnorm() of 1 million people called pop2 where 30% (epsilon=0.3) of the data have an SD of 30 (k=30) .#2.2) Draw 5000 samples of size 30 and put these in sam30. Draw 5000 samples of size 100 and put these in sam100.#2.3) Create variables called sam30means, sam30tmeans, sam100means, sam100tmeans that represent the means AND trimmed means for the samples. #2.4) Use a density plot to show the sampling distribution of the means and trimmed means for these variables.#2.5) Compare the Standard Error (SE) of the sampling distributions. #2.6) Which would be better here: a larger sample size using the mean as the location estimator OR a smaller sample using the trimmed mean? #2.7) Which location estimator performs the best, regardless of sample size?-------------------------------------------------------------------------------------------------------------------------------------------------Lab 5 lecture notes:#Lab 5-Contents# 1. Sampling Distribution of the Mean, # Median, and Trimmed Mean under Normality# 2. Sampling Distribution of the Mean, # Median, and Trimmed Mean under Non-Normality# 3. The Central Limit Theorem# Last week we saw that when we had a Normal or Uniform population, # that the means of random samples taken from that population #were normally distributed.#Today we are going to investigate the distributions of the mean,#median, and trimmed mean from samples coming from Normal # and non-normal populations.#---------------------------------------------------------------------------------# 1. Sampling Distribution of the Mean, Median, # and Trimmed Mean under Normality#--------------------------------------------------------------------------------- #Let's start by generating a standard normal distribution (mean=0, SD=1) for 1 million subjectspop1 = rnorm(1000000, mean=0, sd=1) #We will use this as our population from a normal distribution #*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*##EXERCISE 1-1: #A) Find the mean, median, trimmed mean (using tmean() ), and sd of pop1#B) Draw a density plot of pop1#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*# #A)mean(pop1); median(pop1); tmean(pop1); sd(pop1) #B) plot(density(pop1)) #Like we did last week, we are going to want to take random samples # from our population and then compute a measure of central tendency #(eg. mean, median, trimmed mean) for each sample and examine #the distribution of this measure. #We are going to take 5000 samples of 20 subjectssam1 = matrix(, ncol=5000, nrow=20)#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*## EXERCISE 1-2: Use a loop to draw 5000 samples of size 20 from pop1 # an place the samples in sam1#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#for (ii in 1:5000) {sam1[ , ii] = sample(pop1, 20, replace=TRUE)} # Now that we have our datafile containing all 5000 samples (ie. sam1) # we can begin to create variables for each of our location measures #I'll start us off with the meansam1means = apply(sam1, 2, mean) # number 2 = work in the columns rather than rows#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*## EXERCISE 1-3: Use the apply function to generate # the variables sam1meds (medians) and sam1tmeans (trimmed mean)#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#sam1meds = apply(sam1, 2, median)sam1tmeans = apply(sam1, 2, tmean) #Let's look at the distributions of each of these location estimatorsplot(density(sam1means))lines(density(sam1meds), col="red")lines(density(sam1tmeans), col="blue")abline(v = mean(pop1), lty=2) #Add in a line for the pop1 mean#??????????????????????????????????????????????????????????????##Thought Question 1: Which location estimator performs the best #for data coming from a normal population? Why?#??????????????????????????????????????????????????????????????# # One of the ways we can determine which location estimator # performs the best is by looking at the standard deviation # of the estimator accross all the samples. # The estimator with the lowest SD will have the least amount # of variability accross the samples. # A more common name for the standard deviation of the location # estimator is called the Standard Error or SE#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*## EXERCISE 1-4: Find the Standard Error of the sample means,# medians, and trimmed means. Based upon the SE, which # location estimator is the best for samples coming from# a normal population?#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*# sd(sam1means); sd(sam1meds); sd(sam1tmeans) #The mean performs the best.# In real life, we generally cannot go out an collect multiple samples # from a population, so we compute the Standard Error using a formula: # SE = sd(sample) / sqrt(sample N)#---------------------------------------------------------------------------------# 2. Sampling Distribution of the Mean, Median, # and Trimmed Mean under Non-Normality#---------------------------------------------------------------------------------# Normal distributions generally have very few outliers, # however when outliers begin to occur more frequently so of the # basic assumptions about normal distributions are no longer true # (as we are about to see). # One distribution that is like a normal distribution,# but with more outliers is called a mixed or contaminated # normal distribution and it is a result of two populations mixing together. #*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*# #EXAMPLE 1: "a" will be a mix of TWO populations 1: with SD=1 and 2: with SD=2 a=c(rnorm(5000, 0, 1), rnorm(5000, 0, 2)) #Let's compare this to b, which is from ONE population but with the same parameters of a b=rnorm(10000, mean(a), sd(a))plot(density(a))lines(density(b), col="red") #*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*##??????????????????????????????????????????????????????????????##Thought Question 2: How are a and b from Example 1 different?#??????????????????????????????????????????????????????????????##Thankfully, rather than having to create contaminated normal distributions the hard way, we can just use#a function provided to us by Dr. Wilcox called cnorm()#^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^##Contaminated/Mix Normal Distribution: cnorm(n, epsilon=0.1, k=10)#^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^##Let's look at the options for the contaminated normal distribution:#cnorm() combines two normal distributions: #1) A standard normal (mean=0, sd=1) for 1-epsilon % of the data #2) A normal of mean=0 and sd=k for epsilon % of the data #If we were trying to re-create the variable a we made in example 1 we would have to do:z=cnorm(10000, epsilon=0.5, k=2)plot(density(a))lines(density(z), col="blue")#Which looks very very similar to a! #Let's create a second population called pop2 from a contaminated normal distributionpop2 = cnorm(1000000, epsilon=0.1, k=10) #The mean, sd, and plot of which are:mean(pop2); sd(pop2); plot(density(pop2))#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*##EXERCISE 2:#A) Create an empty matrix called sam2 to contain 5000 samples #of 20 observations each#B) Populate sam2 with 5000 random samples of size 20 from pop2#C) Compute the mean (sam2means), median (sam2meds), #and trimmed mean (sam2tmeans) for each sample#D) Create an overlaid density plot of each sample WITH the pop2 #mean as a verticle line#E) Find the SE of each location estimator#F) Based upon the SE, which location estimator is the best # for samples coming from a contaminated normal distribution#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*# #A) #B) #C) #D) #E) #F)#---------------------------------------------------------------------------------# 3. 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Harvard Stats Homework Using R Lab 5 Help
stats homework using RHomework- lab 5:#The central limit theorem (CLT) states that as the sample size gets sufficiently la ...
Harvard Stats Homework Using R Lab 5 Help
stats homework using RHomework- lab 5:#The central limit theorem (CLT) states that as the sample size gets sufficiently large, the distribution of the sample means will be normally distributed.#In addition, the CLT has been used to justify the fact that for many of our statistics we rely upon computing the mean (not median or trimmed mean) of our samples#There are a few problems with the CLT. #1) How large of a sample is needed#2) It seems that our experiments with the contaminated normal may contradict this.#In this homework assignment you will investigate the CLT further. #PART 1 - The Central Limit Theorem under Normality.#1.1) Simulate a standard normal population of 1 million people called pop1 #1.2) Draw 5000 samples of size 20 and put these in sam20. Draw 5000 samples of size 50 and put these in sam50 .#1.3) Create variables called sam20means and sam50means that contains the means of the samples . Use a density plot to show the sampling distribution of the means for sam20means and sam50means together#1.4) Compare the Standard Error (SE) of the sampling distributions. Which sample size creates better estimates of the population mean (ie. has the lowest SE)? #PART 2 - The Central Limit Theorem under Non-Normality#2.1) Simulate a contaminated normal population using cnorm() of 1 million people called pop2 where 30% (epsilon=0.3) of the data have an SD of 30 (k=30) .#2.2) Draw 5000 samples of size 30 and put these in sam30. Draw 5000 samples of size 100 and put these in sam100.#2.3) Create variables called sam30means, sam30tmeans, sam100means, sam100tmeans that represent the means AND trimmed means for the samples. #2.4) Use a density plot to show the sampling distribution of the means and trimmed means for these variables.#2.5) Compare the Standard Error (SE) of the sampling distributions. #2.6) Which would be better here: a larger sample size using the mean as the location estimator OR a smaller sample using the trimmed mean? #2.7) Which location estimator performs the best, regardless of sample size?-------------------------------------------------------------------------------------------------------------------------------------------------Lab 5 lecture notes:#Lab 5-Contents# 1. Sampling Distribution of the Mean, # Median, and Trimmed Mean under Normality# 2. Sampling Distribution of the Mean, # Median, and Trimmed Mean under Non-Normality# 3. The Central Limit Theorem# Last week we saw that when we had a Normal or Uniform population, # that the means of random samples taken from that population #were normally distributed.#Today we are going to investigate the distributions of the mean,#median, and trimmed mean from samples coming from Normal # and non-normal populations.#---------------------------------------------------------------------------------# 1. Sampling Distribution of the Mean, Median, # and Trimmed Mean under Normality#--------------------------------------------------------------------------------- #Let's start by generating a standard normal distribution (mean=0, SD=1) for 1 million subjectspop1 = rnorm(1000000, mean=0, sd=1) #We will use this as our population from a normal distribution #*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*##EXERCISE 1-1: #A) Find the mean, median, trimmed mean (using tmean() ), and sd of pop1#B) Draw a density plot of pop1#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*# #A)mean(pop1); median(pop1); tmean(pop1); sd(pop1) #B) plot(density(pop1)) #Like we did last week, we are going to want to take random samples # from our population and then compute a measure of central tendency #(eg. mean, median, trimmed mean) for each sample and examine #the distribution of this measure. #We are going to take 5000 samples of 20 subjectssam1 = matrix(, ncol=5000, nrow=20)#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*## EXERCISE 1-2: Use a loop to draw 5000 samples of size 20 from pop1 # an place the samples in sam1#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#for (ii in 1:5000) {sam1[ , ii] = sample(pop1, 20, replace=TRUE)} # Now that we have our datafile containing all 5000 samples (ie. sam1) # we can begin to create variables for each of our location measures #I'll start us off with the meansam1means = apply(sam1, 2, mean) # number 2 = work in the columns rather than rows#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*## EXERCISE 1-3: Use the apply function to generate # the variables sam1meds (medians) and sam1tmeans (trimmed mean)#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#sam1meds = apply(sam1, 2, median)sam1tmeans = apply(sam1, 2, tmean) #Let's look at the distributions of each of these location estimatorsplot(density(sam1means))lines(density(sam1meds), col="red")lines(density(sam1tmeans), col="blue")abline(v = mean(pop1), lty=2) #Add in a line for the pop1 mean#??????????????????????????????????????????????????????????????##Thought Question 1: Which location estimator performs the best #for data coming from a normal population? Why?#??????????????????????????????????????????????????????????????# # One of the ways we can determine which location estimator # performs the best is by looking at the standard deviation # of the estimator accross all the samples. # The estimator with the lowest SD will have the least amount # of variability accross the samples. # A more common name for the standard deviation of the location # estimator is called the Standard Error or SE#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*## EXERCISE 1-4: Find the Standard Error of the sample means,# medians, and trimmed means. Based upon the SE, which # location estimator is the best for samples coming from# a normal population?#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*# sd(sam1means); sd(sam1meds); sd(sam1tmeans) #The mean performs the best.# In real life, we generally cannot go out an collect multiple samples # from a population, so we compute the Standard Error using a formula: # SE = sd(sample) / sqrt(sample N)#---------------------------------------------------------------------------------# 2. Sampling Distribution of the Mean, Median, # and Trimmed Mean under Non-Normality#---------------------------------------------------------------------------------# Normal distributions generally have very few outliers, # however when outliers begin to occur more frequently so of the # basic assumptions about normal distributions are no longer true # (as we are about to see). # One distribution that is like a normal distribution,# but with more outliers is called a mixed or contaminated # normal distribution and it is a result of two populations mixing together. #*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*# #EXAMPLE 1: "a" will be a mix of TWO populations 1: with SD=1 and 2: with SD=2 a=c(rnorm(5000, 0, 1), rnorm(5000, 0, 2)) #Let's compare this to b, which is from ONE population but with the same parameters of a b=rnorm(10000, mean(a), sd(a))plot(density(a))lines(density(b), col="red") #*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*##??????????????????????????????????????????????????????????????##Thought Question 2: How are a and b from Example 1 different?#??????????????????????????????????????????????????????????????##Thankfully, rather than having to create contaminated normal distributions the hard way, we can just use#a function provided to us by Dr. Wilcox called cnorm()#^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^##Contaminated/Mix Normal Distribution: cnorm(n, epsilon=0.1, k=10)#^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^##Let's look at the options for the contaminated normal distribution:#cnorm() combines two normal distributions: #1) A standard normal (mean=0, sd=1) for 1-epsilon % of the data #2) A normal of mean=0 and sd=k for epsilon % of the data #If we were trying to re-create the variable a we made in example 1 we would have to do:z=cnorm(10000, epsilon=0.5, k=2)plot(density(a))lines(density(z), col="blue")#Which looks very very similar to a! #Let's create a second population called pop2 from a contaminated normal distributionpop2 = cnorm(1000000, epsilon=0.1, k=10) #The mean, sd, and plot of which are:mean(pop2); sd(pop2); plot(density(pop2))#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*##EXERCISE 2:#A) Create an empty matrix called sam2 to contain 5000 samples #of 20 observations each#B) Populate sam2 with 5000 random samples of size 20 from pop2#C) Compute the mean (sam2means), median (sam2meds), #and trimmed mean (sam2tmeans) for each sample#D) Create an overlaid density plot of each sample WITH the pop2 #mean as a verticle line#E) Find the SE of each location estimator#F) Based upon the SE, which location estimator is the best # for samples coming from a contaminated normal distribution#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*# #A) #B) #C) #D) #E) #F)#---------------------------------------------------------------------------------# 3. The Central Limit Theorem#--------------------------------------------------------------------------------- #We've discovered a few things today: #1) When a population comes from a normal distribution, # then mean will be the best location estimator of the samples#2) When a population comes from a mixed/contaminated normal distribution, # the trimmed mean is the best location estimator# These observations are related to the Central Limit Theorem (CLT)# that is discussed in Section 5.3 of the book (page 85)# The CLT states that as the sample size gets sufficiently large, # the distribution of the sample means will be normally distributed.# We saw a demonstration of this last week when we looked at the means # from the unifom distribution.# The CLT has been used to justify the fact that for many of our statistics# we rely upon computing the mean (not median or trimmed mean) of our samples#There are a few problems with the CLT. #1) how large of a sample do we need? #2) It seems that our experiements with the contaminated normal may contradict this.#In the homework you will investigate this further
Minimum and Maximum Function Discussion
Select either the minimum or maximum function. Identify a task - personal or professional - that could be modeled mathemat ...
Minimum and Maximum Function Discussion
Select either the minimum or maximum function. Identify a task - personal or professional - that could be modeled mathematically through your chosen function. Explain how the chosen function be used in making good decisions.
Examples of tasks might be:
Make the largest garden possible using a given amount of fencing.
Configure an airplane to create the least amount of drag for an airplane in flight.
Be creative!
MAT 274 Grand Canyon University Probability and Statistics Problems
DQ 1: Use the sample from Topic 2 DQ 1 and test that the population mean for rolling a single die is 3.5.DQ 2: Explain the ...
MAT 274 Grand Canyon University Probability and Statistics Problems
DQ 1: Use the sample from Topic 2 DQ 1 and test that the population mean for rolling a single die is 3.5.DQ 2: Explain the difference between statistical significance and practical significance.I load the paper that include the solution of DQ 1 part A and I need the solution of DQ 1 part B. Please read the paper then answer the DQ 1 . Thanks,Shahram
"Questions to be Graded: Exercise 26" in Statistics for Nursing Research: A Workbook for Evidence-Based Practice
Use MS Word to complete "Questions to be Graded: Exercise 26" in Statistics for Nursing Research: A Workbook for Evidence- ...
"Questions to be Graded: Exercise 26" in Statistics for Nursing Research: A Workbook for Evidence-Based Practice
Use MS Word to complete "Questions to be Graded: Exercise 26" in Statistics for Nursing Research: A Workbook for Evidence-Based Practice. Submit your work in SPSS by copying the output and pasting into the Word document. In addition to the SPSS output, please include explanations of the results where appropriate.
15 Multiple Choice Calculus
1.Which of the following integrals represents the area of the region bounded by x = e and the functions f(x) = ln(x) and g ...
15 Multiple Choice Calculus
1.Which of the following integrals represents the area of the region bounded by x = e and the functions f(x) = ln(x) and g(x) = log1/e(x)? (4 points)2.Which integral gives the area of the region in the first quadrant bounded by the axes, y = ex, x = ey, and the line x = 4? (4 points)3.Find the area of the region bounded by the graphs of y = x2 - 4x and y = x - 4. (4 points)-4.5004.5002.333None of these4.Find the area of the region bounded by the graphs of y = x, y = 4 - 3x, and x = 0. (4 points)0.37524None of these5.Find the number a such that the line x = a divides the region bounded by the curves x = y2 − 1 and the y-axis into 2 regions with equal area. Give your answer correct to 3 decimal places. (4 points)1.Use your calculator to find the approximate volume in cubic units of the solid created when the region under the curve y = cos(x) on the interval [0, ] is rotated around the x-axis. (4 points)10.7852.4673.1422.Find the volume of the solid formed by revolving the region bounded by the graphs of y = x3, x = 2, and y = 1 about the y-axis. (4 points)None of these3.Which of the following integrals correctly computes the volume formed when the region bounded by the curves x2 + y2 = 25, x = 4 and y = 0 is rotated around the y-axis? (4 points)4.The base of a solid in the first quadrant of the xy plane is a right triangle bounded by the coordinate axes and the line x + y = 6. Cross sections of the solid perpendicular to the base are squares. What is the volume, in cubic units, of the solid? (4 points)3618108725.The base of a solid in the region bounded by the two parabolas y2 = 8x and x2 = 8y. Cross sections of the solid perpendicular to the x-axis are semicircles. What is the volume, in cubic units, of the solid? (4 points)8π1.Find the average value of f(x)=e2x over the interval [2, 4]. (4 points)1463.18731.591517.7823.602.Find the velocity, v(t), for an object moving along the x-axis if the acceleration, a(t), is a(t) = cos(t) - sin(t) and v(0) = 3. (4 points)v(t) = sin(t) + cos(t) + 3v(t) = sin(t) + cos(t) + 2v(t) = sin(t) - cos(t) + 3v(t) = sin(t) - cos(t) + 43.Find the distance, in feet, a particle travels in its first 2 seconds of travel, if it moves according to the velocity equation v(t)= 6t2 - 18t + 12 (in feet/sec). (4 points)456-14.For an object whose velocity in ft/sec is given by v(t) = -3t2 + 5, what is its displacement, in feet, on the interval t = 0 to t = 2 secs? (4 points)6.6072-2.3032.3035.A pitcher throws a baseball straight into the air with a velocity of 72 feet/sec. If acceleration due to gravity is -32 ft/sec2, how many seconds after it leaves the pitcher's hand will it take the ball to reach its highest point? Assume the position at time t = 0 is 0 feet. (4 points)2.252.54.254.5
MATH 160 CC Undergraduate Students Sleep Hours in Nighttime Lab Report
Progress CheckUse this activity to assess whether you and your peers can: Under appropriate conditions, conduct a hypothes ...
MATH 160 CC Undergraduate Students Sleep Hours in Nighttime Lab Report
Progress CheckUse this activity to assess whether you and your peers can: Under appropriate conditions, conduct a hypothesis experiment about a difference between two population means. State a conclusion in contextLearn by DoingIn this activity you will learn to use StatCrunch to perform a two-sample t-test.Some features of this activity may not work well on a cell phone or tablet. We highly recommend that you complete this activity on a computer.Use the rubric at the bottom of this page as a guide for completing this assignment.A list of StatCrunch directions is provided after the Prompt section below.DirectionsSubmit your work:Carefully read all sections below (beginning with the Context section and ending with the Prompt section).Commit a good-faith effort to address all items in the Prompt section below. Please be sure to number your responses.If directed to do so, embed all required StatCrunch output in your initial submission. Please do not submit StatCrunch output as an attachment.Complete your assigned peer reviews:After you submit your initial good-faith attempt, continue to the ANSWER(S) page and review your instructor's response. But please do not submit your corrected work yet.Within three days after the due date, return to this assignment and complete your assigned peer reviews (directions (Links to an external site.)).Submit your corrected work:We all learn from mistakes (our own and our classmates' mistakes). So please do not immediately correct your own mistakes. If possible, wait until you receive feedback from at least one of your peers. If necessary, correct your work and resubmit the entire assignment - including any required StatCrunch output. Your instructor will only review and grade your most recent submission, so please do not refer to a previous submission.ContextDo undergraduates sleep less than graduate students?A student conducted a study of sleep habits at a large state university. His hypothesis is that undergraduates will party more and sleep less than graduate students. He surveyed random samples of 75 undergraduate students and 50 graduate students. Subjects reported the hours they sleep in a typical night.For this hypothesis test, he defined the population means as follows:𝜇1μ1μ2 is the mean number of hours undergraduate students sleep in a typical night.𝜇2 is the mean number of hours graduate students sleep in a typical night.VariablesHours: typical number of hours a student sleeps each night Program: undergraduate or graduate Program is the explanatory variable, and the data is categorical. Hours is the response variable, and the data is quantitative.DataDownload the sleep2 (Links to an external site.) datafile, and upload the file in StatCrunch. PromptState the null and alternative hypotheses. Include a clear description of the populations and the variable.Explain why we can safely use the two-sample T-test in this case.Use StatCrunch to carry out the test. (directions)Copy and paste the content of in the StatCrunch output window (text and the table) in your initial post. State a conclusion in the context of this problem.List of StatCrunch DirectionsEach link will open in a new window. To return to this discussion, either close the new tab or select the tab for this discussion. Purchase StatCrunch (You only need to do this once.)Open StatCrunchDownload Excel FileUpload Excel Data File to StatCrunchDownload StatCrunch Output Window (no screenshots; please use these directions)Upload Files to Your Stats-Class Folder in CanvasEmbed Pictures in a Textbox (no attachments; please use these directions)Copy & Paste a StatCrunch Table Conduct a Hypothesis Test for a Difference in Two Population MeansContent by the Open Learning Initiative (Links to an external site.) and licensed under CC BY (Links to an external site.).RubricPeer Reviewed Assignment w/ StatCrunchPeer Reviewed Assignment w/ StatCrunchCriteriaRatingsPtsThis criterion is linked to a Learning OutcomeAddressing the Prompt6 ptsFull MarksAll parts of the Prompt are addressed. Answers are correct. Statistical vocabulary is used appropriately. Writing is clear and thought process is easy to follow.4 ptsPartial CreditSome parts of the prompt are not addressed, are incorrect, or are unclear.0 ptsNo MarksThe prompt is not addressed.6 ptsThis criterion is linked to a Learning OutcomeStatCrunch Data2 ptsFull MarksAppropriate StatCrunch graphs and/or tables are provided as directed.1 ptsPartial CreditStatCrunch graphs and tables are inappropriate or missing important information.0 ptsNo MarksNo StatCrunch information is provided.2 ptsThis criterion is linked to a Learning OutcomeIndividual Penalty0 ptsNo individual penalty-1 ptsIndividual penalty.Please see the instructor comments for more information.0 ptsThis criterion is linked to a Learning OutcomePeer Reviews2 ptsFull MarksYou completed all assigned peer reviews (maximum of 2). For each peer review, the points you assigned in the rubric are appropriate. You included comments explaining the score you posted in the rubric. If you deducted points in the rubric, your comments explain what the author needs to do to earn a higher grade when the teacher grades the assignment.1 ptsPartial CreditCommitted a good-faith effort to provide a high-quality peer review, but many necessary instructive comments are missing.0 ptsNo MarksNo peer review provided or the comments are not instructive.2 ptsTotal Points: 10
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