The following observations are lifetimes (days) subsequent to diagnosis for individuals suffering from blood cancer. 116 182 256 418 441 461 866 924 983 1026 1063 1063 1278 1291 1358 1369 1409 1603 1605 1696 1736 1799 1815 1853 1899 517 739 743 789 808 1165 1191 1222 1222 1251 1455 1479 1519 1578 1578 1599 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.] Yes, the range is sufficiently large enough for the confidence interval to be reasonable. No, we need to assume that the population is normally distributed. No, the range is not large enough for the confidence interval to be reasonable. Yes, the sample size is large enough for the confidence interval to be reasonable. No, the sample size is not large enough for the confidence interval to be reasonable. (b) Calculate and interpret a confidence interval with a 99% confidence level for true average lifetime. [Hint: x = 1192.0 and s= 506.5.] (Round your answers to one decimal place.) Interpret the resulting interval. We are 99% confident that the true population mean lies below this interval. ○ We are 99% confident that the true population mean lies above this interval. We are 99% confident that this interval does not contain the true population mean

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