Question

Suppose the lifelengths in hours of lightbulbs from a manufacturing process are known to be distributed...

Suppose the lifelengths in hours of lightbulbs from a manufacturing process are
known to be distributed Gamma(2, θ), where θ ∈ (0,∞) is unknown. A random
sample of 27 bulbs was taken and their lifelengths measured with the following data
obtained.

336.87 2750.71 2199.44 292.99 1835.55 1385.36 2690.52
710.64 2162.01 1856.47 2225.68 3524.23 2618.51 361.68
979.54 2159.18 1908.94 1397.96 914.41 1548.48 1801.84
1016.16 1666.71 1196.42 1225.68 2422.53 753.24


Determine an approximate 0.90-confidence interval for θ.

The answer is (9.5413 × 10^−4, 1.5045 × 10^−3). Can anyone explain why?

Math   Statistics-And-Probability   
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