The built-in data set mtcars compares 11 aspects of automobile design 32 different 1974 model automobiles. We will be looking at the mpg column of mtcars. Assume that the 32 cars are a random sample of all 1974 automobiles. We would like to estimate the true mean value, μ, of the mpg using this data. Using R we can convert this data into the vector x by the assignment x<-mtcars$mpg. Assume that the n measurements x=(X₁, X2,...,xn) are a random sample from a population with true unknown mean μ and true unknown variance ². Remember, x<-mtcars$mpg a) Calculate, n, the number of elements in x. b) Calculate the sample variance deviation of x. c) Estimate true mean μ, using this data by calculating the sample mean. d) Calculate the sample standard deviation ,s, of x e) Assuming normality of the mtcars$mpg data, calculate the maximum likelihood estimate of u? f) Calculate the 64th percentile of x using the R quantile function. g) Calculate a 16 trimmed mean for x using R.

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
icon
Related questions
Question

please answer all questions fully and show all work down to the numerical values for each part

The built-in data set mtcars compares 11 aspects of automobile design for 32 different 1974 model automobiles. We will be looking at the mpg column of mtcars. Assume that the 32 cars
are a random sample of all 1974 automobiles. We would like to estimate the true mean value, µ, of the mpg using this data. Using R we can convert this data into the vector x by the
assignment x<-mtcars$mpg. Assume that the n measurements x=( X₁, X2,...,xn) are a random sample from a population with true unknown mean μ and true unknown variance ².
Remember, x<-mtcars$mpg
a) Calculate, n, the number of elements in x.
b) Calculate the sample variance deviation of x.
c) Estimate true mean μ, using this data by calculating the sample mean.
d) Calculate the sample standard deviation,s, of x
e) Assuming normality of the mtcars$mpg data, calculate the maximum likelihood estimate of µ?
f) Calculate the 64th percentile of x using the R quantile function.
1
g) Calculate a trimmed mean for x using R.
16
h) Since the sample size is >30 we can create a confidence interval for μ using a normal critical value. If we want the confidence interval to be at the 95% level and we use a normal
critical value, then what critical value should we use?
i) Calculate a 95% confidence interval(using a normal critical value) for µ.
(
j) How long is the 95% confidence interval just created in part i?
k) Copy your R script for the above into the text box here.
Transcribed Image Text:The built-in data set mtcars compares 11 aspects of automobile design for 32 different 1974 model automobiles. We will be looking at the mpg column of mtcars. Assume that the 32 cars are a random sample of all 1974 automobiles. We would like to estimate the true mean value, µ, of the mpg using this data. Using R we can convert this data into the vector x by the assignment x<-mtcars$mpg. Assume that the n measurements x=( X₁, X2,...,xn) are a random sample from a population with true unknown mean μ and true unknown variance ². Remember, x<-mtcars$mpg a) Calculate, n, the number of elements in x. b) Calculate the sample variance deviation of x. c) Estimate true mean μ, using this data by calculating the sample mean. d) Calculate the sample standard deviation,s, of x e) Assuming normality of the mtcars$mpg data, calculate the maximum likelihood estimate of µ? f) Calculate the 64th percentile of x using the R quantile function. 1 g) Calculate a trimmed mean for x using R. 16 h) Since the sample size is >30 we can create a confidence interval for μ using a normal critical value. If we want the confidence interval to be at the 95% level and we use a normal critical value, then what critical value should we use? i) Calculate a 95% confidence interval(using a normal critical value) for µ. ( j) How long is the 95% confidence interval just created in part i? k) Copy your R script for the above into the text box here.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps

Blurred answer
Similar questions
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman