The following observations are lifetimes (days) subsequent to diagnosis for individuals suffering from blood cancer. 115 181 255 418 442 462 516 739 743 789 807 865 925 984 1026 1062 1063 1166 1191 1222 1222 1252 1278 1291 1358 1369 1409 1455 1479 1519 1578 1578 1599 1603 1606 1696 1736 1799 1815 1852 1899 1925 1965 (a) Can a confidence interval for true average lifetime be calculated without assuming anything about the nature of the lifetime distribution? Explain your reasoning. [Note: A normal probability plot of the data exhibits a reasonably linear pattern.] O Yes, the sample size is large enough for the confidence interval to be reasonable. O No, the range is not large enough for the confidence interval to be reasonable. O No, the sample size is not large enough for the confidence interval to be reasonable. O Yes, the range is sufficiently large enough for the confidence interval to be reasonable. O No, we need to assume that the population is normally distributed. (b) Calculate and interpret a confidence interval with a 99% confidence level for true average lifetime. [Hint: x = 1192.0 and s = 506.6.] (Round your answers to one decimal place.) Interpret the resulting interval. O We are 99% confident that the true population mean lies above this interval. O We are 99% confident that the true population mean lies below this interval. We are 99% confident that this interval does not contain the true population mean. O We are 99% confident that this interval contains the true population mean. You may need to use the appropriate table in the Appendix of Tables to answer this