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 Annual Numbers Of Lynx Trappings From 1821 To 1934 In Canada We Can 1 (226.28 KiB) Viewed 28 times

The built-in lynx data set is a time series giving annual numbers of lynx trappings from 1821 to 1934 in Canada. We can easily access this data with the assignment x<-as.vector(lynx). Assume these values are a random sample from a normal population with unknown mean μ and unknown standard deviation o. Call the vector of observations x, using the assignment above x<-as.vector(lynx) a) Calculate the sum of the first 15 elements of x. b) Calculate the maximum value of the first 15 elements 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 √7x. i) If we assume that the population has a normal distribution, then calculate the maximum likelihood estimate of 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 a 92% 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 92% prediction interval for μ, noting that the sample size is large enough so we can use a normal distribution critical value zstar. Note μ can be negative. ( ) X - 1535 m) Using this data, we create an 8% level test of Ho: μ=1535 versus the alternative H₂: > 1535. We will reject Ho if z = is the value 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 the test. p) Copy your R script for the above into the text box here. √114 ) > zstar where s is the sample standard deviation. What