The following observations are lifetimes (days) subsequent to diagnosis for individuals suffering from blood cancer ("A Goodness of Fit Approach to the Class of Life Distributions with Unknown Age," Quality and Reliability Engr. Intl., 2012:761−766):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. 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 data exhibits a reasonably linear pattern.] b) Calculate and interpret a confidence interval with a 99% confidence level for true average lifetime. [Hint: mean =1191.6,s=506.6.]

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The following observations are lifetimes (days) subsequent to diagnosis for individuals suffering from blood cancer (&quot;A Goodness of Fit Approach to the Class of Life Distributions with Unknown Age,&quot; Quality and Reliability Engr. Intl., 2012:761−766):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. 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 data exhibits a reasonably linear pattern.] b) Calculate and interpret a confidence interval with a 99% confidence level for true average lifetime. [Hint: mean =1191.6,s=506.6.]

doplovif · Accepted Answer

From the given information,  Sample data:  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  Since, sample size is greater than 30 but population standard deviation is not known therefore t-distribution will be most suitable here. (Though some statistician would use Z as well because by CLT, sample standard deviation can be approximated to population standard deviation)  b) The 99% confidence interval for the average lifetime can be calculated as:  The mean and standard deviation can be computed as:  x―=∑xn  =115+181+………….196543  =1186.279  s=∑(xi−x―i)2n−1  =(115−1186.279)2+…………+(1965−1186.279)243−1  =506.1959  CRITICAL VALUE:  Thus, confidence interval:  CI=x―±tα,df×sn  =1186.279±2.419×506.195943  (999.546,1373.011)  Interpretation: This confidence interval shows that the 99% of the times true population mean will fall in the interval or with repeated sampling the 0.99 probability that true average of lifetime will lie in the (999.546,1373.011).

The following observations are lifetimes (days) subsequent to diagnosis for individuals suffering from blood cancer ("A Goodness of Fit Approach to the Class of Life Distributions with Unknown Age,"

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