The following observations are lifetimes (days) subsequent to diagnosis for individuals suffering from blood cancer

115, 181, 255, 418, 441, 461, 516, 739, 743, 789, 807, 865, 924, 983
1025, 1062, 1063, 1165, 1191, 1222, 1222, 1251, 1277, 1290, 1357
1369, 1408, 1455, 1278, 1519, 1578, 1578, 1599, 1603, 1605
1696, 1735, 1799, 1815, 1852, 1899, 1925, 1965.

Can a confidence interval for true average lifetime be calculated without assuming anything about the nature of the lifetime distribution? Explain your reasoning.