The built-in UKgas data set is a time series of UK gas consumption from 1960Q1 to 1986Q4, in millions of therms. We can easily convert this data to a vector with the assignment x<-as.vector(UKgas). Assume these values are a random sample from a normal population with unknown mean and unknown standard deviation o. Call the vector of observations x (using the assignment above x <-as.vector(UKgas)) a) Calculate the sum of the first 12 elements of x.?[ b) What is the maximum value of x. [ c) Calculate the sample mean of x. d) Calculate the sample variance of x. e) Calculate the sample standard deviations of x. [ f) Calculate the sample median of x using R. 9) Calculate the interquartile range of x, using R. h) Calculate the sample variance of 0.5x. i) Calculate the sum of the squares of the 1st 12 elements of x j) Calculate the sum of the square roots of the 1st 12 elements of x.[ k) Using this data, create an 90% confidence interval for , noting that the sample size is large enough so we can use a normal distribution critical value zstar.( 1) Using this data, create a 90% prediction interval for , noting that the sample size is large enough so we can use a normal distribution critical value zstar and that it is possible to predict a negative number for gas consumptiom.. x - 325 m) Using this data, we create a 10% level test of Ho: =325 versus the alternative Ha: > 325. We will reject Ho if z = n) Continuing from part m, what is the value of z?[ o) Continuing from parts m and n, what is the p value of the test. p) Copy your R script for the above into the text box here. > zstar where s is the sample standard deviation. What is the value of zstar? (Calculate from normal distribution) 108
The built-in UKgas data set is a time series of UK gas consumption from 1960Q1 to 1986Q4, in millions of therms. We can easily convert this data to a vector with the assignment x<-as.vector(UKgas). Assume these values are a random sample from a normal population with unknown mean and unknown standard deviation o. Call the vector of observations x (using the assignment above x <-as.vector(UKgas)) a) Calculate the sum of the first 12 elements of x.?[ b) What is the maximum value of x. [ c) Calculate the sample mean of x. d) Calculate the sample variance of x. e) Calculate the sample standard deviations of x. [ f) Calculate the sample median of x using R. 9) Calculate the interquartile range of x, using R. h) Calculate the sample variance of 0.5x. i) Calculate the sum of the squares of the 1st 12 elements of x j) Calculate the sum of the square roots of the 1st 12 elements of x.[ k) Using this data, create an 90% confidence interval for , noting that the sample size is large enough so we can use a normal distribution critical value zstar.( 1) Using this data, create a 90% prediction interval for , noting that the sample size is large enough so we can use a normal distribution critical value zstar and that it is possible to predict a negative number for gas consumptiom.. x - 325 m) Using this data, we create a 10% level test of Ho: =325 versus the alternative Ha: > 325. We will reject Ho if z = n) Continuing from part m, what is the value of z?[ o) Continuing from parts m and n, what is the p value of the test. p) Copy your R script for the above into the text box here. > zstar where s is the sample standard deviation. What is the value of zstar? (Calculate from normal distribution) 108
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Transcribed Image Text:The built-in UKgas data set is a time series of UK gas consumption from 1960Q1 to 1986Q4, in millions of therms. We can easily convert this data to a vector with the assignment x<-as.vector(UKgas).
Assume these values are a random sample from a normal population with unknown mean and unknown standard deviation 0.
Call the vector of observations x (using the assignment above x <- as.vector(UKgas))
a) Calculate the sum of the first 12 elements of x.?
b) What is the maximum value of x.
c) Calculate the sample mean of x.
d) Calculate the sample variance of x.
e) Calculate the sample standard deviations of x.
f) Calculate the sample median of x using R.
g) Calculate the interquartile range of x, using R.
h) Calculate the sample variance of 0.5x.
i) Calculate the sum of the squares of the 1st 12 elements of x
j) Calculate the sum of the square roots of the 1st 12 elements of x.
k) Using this data, create an 90% confidence interval for μ, noting that the sample size is large enough so we can use a normal distribution critical value zstar.(
1) Using this data, create a 90% prediction interval for , noting that the sample size is large enough so we can use a normal distribution critical value zstar and that it is possible to predict a negative number for gas consumptiom.. (
x - 325
S
m) Using this data, we create a 10% level test of Ho: μ=325 versus the alternative H₂: > 325. We will reject Ho if z =
n) Continuing from part m, what is the value of z?
o) Continuing from parts m and n, what is the p value of the test.
p) Copy your R script for the above into the text box here.
108
>zstar where s is the sample standard deviation. What is the value of zstar? (Calculate from normal distribution)
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