Question

The following observations are lifetimes (days) subsequent to diagnosis for individuals suffering from blood cancer. - 80 115 866 1277 1603 181 924 1291 1605 256 983 1358 1697 418 1025 1369 1736 441 1062 1409 1799 462 1064 1456 1815 517 739 11651191 1478 1519 1853 1899 744 1222 1578 1925 789 1222 1578 808 1252 1599 1966 (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 sample size is large enough for the confidence interval to be reasonable. Yes, the range is sufficiently large enough for the confidence interval to be reasonable. No, the sample size is not large enough for the confidence interval to be reasonable. No, the range is not large enough for the confidence interval to be reasonable. 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. We are 99% confident that this interval does not contain the true population mean. We are 99% confident that the true population mean lies above this interval. We are 99% confident that this interval contains the true population mean. We are 99% confident that the true population mean lies below this interval. You may need to use the appropriate table in the Appendix of Tables to answer this question.

Answer 1

The statistical software output for this problem is:

One sample T summary confidence interval: u:Mean of population 99% confidence interval results: Mean Sample Mean Std. Err. DF L. Limit U. Limit 1192 77.255776 42 983.5588 1400.4412

Hence,

a) Option A is correct.

b) 99% confidence interval:

(983.6, 1400.4)

Option C is correct.