Finish the following questions using R and R commander. Make sure that you copy and paste the computer outputs into the space below each question and write down your answers in statements. Graphs should include titles and axis labels, as appropriate. 1. For the following variables of interest, i) Use R to create a normal probability plot and a histogram. Paste your work into your report ii) Describe your findings. In particular, do the graphs provide evidence against the assumption of a normally distributed population? iii) Based on your descriptions (as well as the sample size n), determine if one mean inference is valid, and whether z-procedures or t-procedures should be employed. For each dataset, you may assume the data are obtained via random sampling and that the population standard deviation is unknown. a) The dataset "School100.xIsx" contains information regarding a sample of 100 schools from Great Britain. The variable of interest is GPS_AVERAGE (average grammar scores on an aptitude test for students at that school). (3 marks) b) The dataset "Beer21.xIsx" contains information regarding a sample of 21 beers brands in the United States. The variable of interest is abv (alcohol by volume) for the beer brands. (3 marks) c) In the above work, we did not examine the boxplots for the considered samples. What can a boxplot show us that cannot be seen in a normal probability plot or histogram? (2 marks) 2. This question uses datasets examined in Question 1. You may reference work from Question 1 when deciding what test to perform. For each hypothesis test, provide a full write-up that includes your hypotheses, level of significance, statement and discussion of the assumptions, test statistic, p-value, decision, and conclusion. Use R commander to obtain the relevant output needed to complete the test. a) Return to the dataset "Beer21.xIsx." Test if the mean ABV of beer is greater than 0.05 in the United States. Use a significance level of 2%. (7 marks) b) Return to the dataset "School100.xlsx." Test if average grammar scores differ from 105 on aptitude tests at British schools. Use a significance level of 1%. (7 marks)c] Return to the dataset "Schoollililxlsx" Compute and interpret a 99% condence interval for mean grammar scores. Does the interval provide evidence that the average grammar score differs from 11215 on aptitude tests at British Schools? Explain. [5 marks] d] Did you reach the same conclusion in part b] and in part c]? Explain your answer. [2 marks]