(d) When the sample size is small, an alternative method for calculating a 95% confidence interval for a proportion involves adding 2 successes and 2 failures to the sample, calculating the value of P using the original sample plus these 4 additional observations, and using the formula: p+1.96, P (1- p) n (i) In the consumer organization's sample of 5 cars, I had engine trouble in the first 100,000 miles. What is the value of P that should be used to calculate the confidence interval for this sample, assuming that the alternative method is to be used? I (ii) The table below shows the results of the simulation from part (c), along with the new lower and upper 95% confidence interval boundaries using the alternative method. P = proportion of Numbe Alternative Alternative cars in the sample r of lower 95% upper 95% with engine sample confidence confidence trouble S boundary boundary 0 168 -0.049 0.494 0.2 360 0.025 0.641 0.4 309 0.120 0.769 0.6 133 0.231 0.880 0.8 28 0.359 0.975 1 2 0.506 1.049 According to the simulation, does the alternative method work better than the traditional method in this context? Explain your reasoning