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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.

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.

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
6th Edition
ISBN:9781337111348
Author:Bruce Crauder, Benny Evans, Alan Noell
Publisher:Bruce Crauder, Benny Evans, Alan Noell
Chapter5: A Survey Of Other Common Functions
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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.
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