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In: Statistics and Probability

An article in Cancer Research “Analyses of littermatched time-to-response data, with modifications for recovery of interlitter...

An article in Cancer Research “Analyses of littermatched time-to-response data, with modifications for recovery of interlitter information,” (1977, Vol. 37, pp. 3863–3868) tested the tumorigenesis of a drug. A total of 41 rats were randomly selected from litters and given the drug. The times of tumor appearance were recorded as follows: 101, 104, 104, 77, 89, 88, 104, 96, 82, 70, 89, 91, 39, 103, 93, 85, 104, 104, 81, 67, 104, 104, 104, 87, 104, 89, 78, 104, 86, 76, 103, 102, 80, 45, 94, 104, 104, 76, 80, 72, 73 Calculate a 95% confidence interval on the standard deviation of time until a tumor appearance. Assume population is approximately normally distributed. Round your answers to 2 decimal places.

Solutions

Expert Solution

Values ( X ) Σ ( Xi- X̅ )2
101 149.3162
104 231.6332
104 231.6332
77 138.7802
89 0.0482
88 0.6092
104 231.6332
96 52.1212
82 45.9752
70 352.7072
89 0.0482
91 4.9262
39 2478.0982
103 202.1942
93 17.8042
85 14.2922
104 231.6332
104 231.6332
81 60.5362
67 474.3902
104 231.6332
104 231.6332
104 231.6332
87 3.1702
104 231.6332
89 0.0482
78 116.2192
104 231.6332
86 7.7312
76 163.3412
103 202.1942
102 174.7552
80 77.0972
45 1916.7322
94 27.2432
104 231.6332
104 231.6332
76 163.3412
80 77.0972
72 281.5852
73 249.0242
Total 3640 10231.0252

Mean X̅ = Σ Xi / n
X̅ = 3640 / 41 = 88.7805
Sample Standard deviation SX = √ ( (Xi - X̅ )2 / n - 1 )
SX = √ ( 10231.0252 / 41 -1 ) = 15.993



χ2 (0.05/2, 41 - 1) = 59.3417
χ2 (1 - 0.05/2) , 41 - 1 ) = 24.433
Lower Limit = (( 41-1 ) 255.776 / χ2 (0.05/2) ) = 172.4089
Upper Limit = (( 41-1 ) 255.776 / χ2 (0.05/2) ) = 418.7386
95% Confidence interval is ( 172.4089 , 418.7386 )

95% Confidence interval for standard deviation is  ( 13.13 < σ < 20.46 ).


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