Question One [13 marks] Telsa is an electric vehicle company that manufactures battery powered cars. The quality control manager at the electric car battery factory is interested in how many years a battery will last in a car before failing (and needing replacement). She takes a sample of n = 48 batteries and subjects them to accelerated testing to simulate many years of use. She notes the number of simulated years before failure for each battery and arranges these values in ascending order and enters them into the following table. 4 4 5 5 5 5 5 6 6 6 7 7 7 8 8 8 8 8 8 8 9 9 9 9 9 10 10 10 10 10 10 10 11 11 11 11 11 11 12 12 12 12 13 13 13 For this sample of n = 48 values the following two sums were calculated Ex, =411 and Ex, =3855 Using this information , answer the following questions. (a) Calculate the mean , the median and the mode. Briefly explain what these values tell us about the shape of the distribution of these values. [4 marks] (b) Calculate the unbiased estimate of the standard deviation and the coefficient of variation and briefly interpret your results. [3 marks] (c) An outlier is defined as any value that has a Z score which is either less than -2.5 or greater than +2.5. The Telsa manager thinks that when outliers are present in the data that the values of some descriptive statistics will be distorted by the presence of these outliers. Using the results from part (a) and part (b) of this question calculate the Z scores you need to identify which if any of the 48 values are outliers? State which if any of the values are outliers. Hint: Use the sample estimates from (a) and (b) instead of wand o in the Z-score formula and start by checking of the most extreme observations are outliers. [3 marks] (d) Suppose the chief engineer finds that the data supplied to the manager is systematically biased. The values in the above table are incorrectly deflated (reduced) by 25% , so the first value of 4 should actually be 5 etc. What values should the mean , the median , the mode and the standard deviation have if the correct values are 25% more than the values we have used. [3 marks] Total marks : 13=4+3+3+3