Question

CAN YOU PLEASE POST THE R-SCRIPT ONLY

The built-in data set LakeHuron is a time series which provides records of annual measurements of the level, in feet, of Lake Huron 1875 to 1972. Using R we can convert this data into the vector x by the assignment x<-as.vector(LakeHuron). Assume that the n measurements x=(

x₁, x₂,...,x_n) are a random sample from a population with true unknown mean μ and true unknown variance σ². Remember, let x be defined by x<-as.vector(LakeHuron)

CAN YOU PLEASE POST THE R-SCRIPT ONLY
a) Calculate, n, the number of elements in x.

b)Calculate the sample standard deviation s, of x.

c) Estimate true mean μ, using this data by calculating the sample mean.

d) Calculate an unbiased point estimate of the population variance, σ² of faithful waiting times.

e) Assuming normality of LakeHuron levels, calculate the maximum likelihood estimate of μ?

f) Calculate the 70th percentile of x using R.

Calculate a 2/98 trimmed mean for x using R.

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 97% level and we use a normal critical value, then what critical value should we use?

i) Calculate a 97% confidence interval(using a normal critical value) for μ.
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j) How long is the 97% confidence interval just created in part i?

Answer 1