Using the fact that \(2 T_{r} / \mu\) is a value of a random variable having the chi square distribution with \(2 r\) degrees of freedom, derive the confidence interval for \(\mu\) given on page 511.

Data From Page 511

    

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EXAMPLE 3 Obtaining a confidence interval for mean life Suppose that 50 units are placed on life test (without replacement) and the test is to be truncated after r = 10 of them have failed. We shall suppose, furthermore, that the first 10 failure times are 65, 110, 380, 420, 505, 580, 650, 840, 910, and 950 hours. Estimate the mean life of the component, and its failure rate, and calculate a 90% confidence interval for u.