Statistics Per X google.com/u/0/w/MTlyNTcxMjYyOTEz/t/all To investigate what happens when calculating a confidence interval for a proportion with a small sample size, 1000 simulated random samples of 5 cars were selected from a population of cars where 30% would have engine trouble within the first 100,000 miles. The table summarizes the distribution of P = the proportion of cars in the sample with engine trouble for these 1000 simulated samples. For each possible value of P , the tabl also displays the lower and upper endpoints of a 95% confidence interval for p using the formula: p+1.96 P(1-P) 5 For example, in 309 of the 1000 simulated samples, the value of P was 0.4 with a corresponding confidence interval of -0.029 to 0.829. P = proportion of Numbe cars in the sample r of Lower 95% Upper 95% with engine confidence sample confidence trouble boundary S boundary 0 168 0 0 0.2 360 -0.151 0.551 0.4 309 -0.029 0.829 0.6 133 0.171 1.029 0.8 28 0.449 1.151 1 2 1 1 5 (c) According to the simulation, how often will these 95% confidence intervals capture the true proportion of cars of this type that will have engine trouble in the first 100,000 miles? Explain how you determined your answer. Page 5