Question 1 One of the major oil distribution companies conducted a study recently to estimate the mean quantity of high speed petrol purchased by customers of a particular brand of car per visit to a petrol pump station. To do this, a random sample of customers was selected with the following data being recorded that show the liters of high speed petrol purchased by owners of that particular brand of car. \begin{tabular}{ICCCCCCCCCC) \hline $24.2$ & $22.3$ & $19.9$ & $13.3$ & $18.9$ & $18.7$ & $22.4$ & $29.5$ & $23.4$ & $18.1$ \hline 22 & $24.4$ & 35 & 30 & $24.9$ & $21.2$ & $24.4$ & $34.7$ & 29 & $24.0$ Thline $15.1$ & $21.3$ & $28.4$ & $22.5$ & $15.9$ & $15.7$ & $25.7$ & $28.9$ & $27.1$ & $25.7$ \hline \end{tabular (a) Based on these sample data, construct and interpret a 95 percent confidence interval estimate for the population mean. (b) A manager in that oil company is interested in estimating the mean herself through another sample survey and wants to develop a confidence interval estimate. Suppose, she has determined the required sample size and feels that she cannot afford one that large. What options are available? SP.PC. 1411