D - F The built-in LakeHuron data set is a time series giving the annual measurements of the level, in feet, of Lake Huron 18751972. We can easily access this data with the assignment x<-as.vector(LakeHuron).Assume these values are a random sample from a normal population with unknown mean u and unknown standard deviation o.Call the vector of observations x,using the assignment x<-as.vector(LakeHuron)a) Calculate the sum of the first 15 elements of x.?b) Calculate the minimum value of x.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 3x.i) Calculate an unbiased estimate of the population variance, o using this data.j) If we assume that the population has a normal distribution, then calculate the maximum likelihood estimate of o using this data.k) Using this data, create an 96% confidence interval for u, noting that the sample size is large enough so we can use a normal distribution critical value zstar.(I) Using this data, create a 96% prediction interval for u, noting that the sample size is large enough so we can use a normal distribution critical value zstar. ()X - 578.8m) Using this data, we create a 4% level test of Ho: µ=578.8 versus the alternative Ha: µ > 578.8. We will reject Ho if z => zstar where s is the sample standard deviation. What is the value of zstar? (Calculate from normal distribution)98,n) Continuing from part m, what is the value of z?o) Continuing from parts m and n, what is thep value of the test.

As the student wants the answer to only d,e, and f. So, I provide the answers to those only using R.> x = as.vector(LakeHuron) # It assign the dataset LakeHuron to x.> var(x) # It calculates the variance of x.[1] 1.737911 # It is the variance of x.> sqrt(var(x)) # It calculates the square root of variance of x, Hence, It is the standard deviation of x.[1] 1.318299 # It is the standard deviation of x.> median(x) # It calculates the median of x.[1] 579.12 # It is the median of x.