Q5 (15 points) Continuing the scenario from the previous question, let's look at Lucy and Lei's...

 
 

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Q5 (15 points) Continuing the scenario from the previous question, let's look at Lucy and Lei's waiting time data: waiting.csv. Part (i) Run this code to load and to transform the data. Make sure the data file is in your working directory before you run the code. waiting <- read_csv("./waiting.csv") customers1 <- tibble (waiting) %>% mutate (totaltime = cumsum (waitingtime), numberofminutes = ceiling (totaltime)) %>% group_by (numberofminutes) %>% summarize (numberofcustomers = n()) zeroes <- tibble (numberofminutes = 1:max(customers1$numberofminutes)) customers <- zeroes %>% left join (customers1, by = "numberofminutes") %>% replace_na(list (numberofcustomers = 0)) What is the variable name for the Y;'s? What is the value of m? Part (ii) For the random sample Y₁,..., Y. it can be shown that Ho ~N (0, #) where it is the MLE from Question 4. Compute a 95% confidence interval for using this asymptotic distribution and the observed values of the random sample Y₁,..., Ym. Part (iii) Compute the likelihood ratio A based on the sample Y₁,..., Ym and evaluate the claim that μ = 2, that is, two customers enter the shop per minute. Is this claim supported by the data? Part (iv) Use a bootstrap procedure to estimate a p-value corresponding to the claim that μ = 2 based on Y₁,..., Ym. Is your value different than what you got in Part (iii)? Say why you would expect them to be the same OR explain why they are different. Q5 (15 points) Continuing the scenario from the previous question, let's look at Lucy and Lei's waiting time data: waiting.csv. Part (i) Run this code to load and to transform the data. Make sure the data file is in your working directory before you run the code. waiting <- read_csv("./waiting.csv") customers1 <- tibble (waiting) %>% mutate (totaltime = cumsum (waitingtime), numberofminutes = ceiling (totaltime)) %>% group_by (numberofminutes) %>% summarize (numberofcustomers = n()) zeroes <- tibble (numberofminutes = 1:max(customers1$numberofminutes)) customers <- zeroes %>% left join (customers1, by = "numberofminutes") %>% replace_na(list (numberofcustomers = 0)) What is the variable name for the Y;'s? What is the value of m? Part (ii) For the random sample Y₁,..., Y. it can be shown that Ho ~N (0, #) where it is the MLE from Question 4. Compute a 95% confidence interval for using this asymptotic distribution and the observed values of the random sample Y₁,..., Ym. Part (iii) Compute the likelihood ratio A based on the sample Y₁,..., Ym and evaluate the claim that μ = 2, that is, two customers enter the shop per minute. Is this claim supported by the data? Part (iv) Use a bootstrap procedure to estimate a p-value corresponding to the claim that μ = 2 based on Y₁,..., Ym. Is your value different than what you got in Part (iii)? Say why you would expect them to be the same OR explain why they are different.

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Part i The variable name for the Ys is numberofcustomers and m is the total number of observations t... View the full answer