Question

A random sample of failure time of 49 kidney transplants (in months) is given: 5.27 43.72 3.96 20.34 44.06 31.18 21.98 34.99 39.36 3.39 23.42 43.41 34.35 46.71 64.87 4.53 7.02 40.50 7.38 37.74 13.49 68.48 48.74 12.85 24.15 27.33 4.82 20.00 55.28 20.83 24.13 11.80 13.82 31.55 36.69 52.57 12.45 40.07 16.86 15.54 15.54 3.85 4.08 5.62 17.44 3.38 41.61 29.52 21.61 If we assume failure time has a Gamma distribution answer the following questions (with 2 decimal points). . Find the critical value for the test (for significance level of 0.1).

Answer 1

Critical value ≈ 1.299

Explanation:

number of Kidney transplant ( n ) = 49

Determine the critical value for the test

the sample mean = ∑ failure time / n = 1252.28 / 49 = 25.56

next we determine the standard deviation of the sample

s =
`√(1/(n-1)(xi -X ) ^2)` = 17.3126

standard error = s / √n = 17.3126 / 7 = 2.4732

Given a significance level of 0.1

df (degree of freedom ) = n -1 = 49 - 1 = 48

∝ = 0.1

critical value = 1.299 ( using excel function ; =T.INV(0.90,48) )