The built-in lynx data set is a time series giving annual numbers of lynx trappings from 1821 to 1934 in Canada. We can

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The built-in lynx data set is a time series giving annualnumbers of lynx trappings from 1821 to 1934 in Canada. We caneasily access this data with the assignmentx<-as.vector(lynx).Assume these values are a random sample from a normal populationwith unknown mean 𝜇 and unknown standarddeviation 𝜎.Call the vector of observations x, using the assignment abovex<-as.vector(lynx)a) Calculate the sum of the first 15 elements of x. b) Calculate the maximum value of the first 15 elements ofx. c) Calculate the sample mean of x. d) Calculate the sample variance of x. e) Calculate the sample standard deviation s 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
x. i) If we assume that the population has a normal distribution, thencalculate the maximum likelihood estimate of
𝜎2
using this data. j) If we assume that the population has a normal distribution, thencalculate the maximum likelihood estimate of 𝜎 using thisdata. k) Using this data, create a 92% confidence interval for 𝜇,noting that the sample size is large enough so we can use a normaldistribution critical value zstar.(
,
)l) Using this data, create a 92% prediction interval for 𝜇,noting that the sample size is large enough so we can use a normaldistribution critical value zstar. Note 𝜇 can benegative. (
,
)m) Using this data, we create an 8% level test of
H0: 𝜇=1535 versus the alternative Ha: 𝜇 >1535. We will reject H0 if z =
> zstar
where s is the sample standard deviation. What is thevalue of zstar? (Calculate from normal distribution) n) Continuing from part m, what is the value of z? o) Continuing from parts m and n, what is the p value of thetest. p) Copy your R script for the above into the text box here.