Multiply censored normal samples. The appliance cord data in Table 2.1 of Chapter 1 1 are analyzed as follows to compare the samples from the three tests. The following table summarizes the results of ML fitting a normal distribution to the separate and combined samples.
(a) Calculate the log likelihood ratio test statistic for equality of the three standard deviations, assuming the means differ. Compare it with an appropriate chi-square percentile and state your conclusions.
(b) Calculate the log likelihood ratio test statistic for equality of the three means, assuming the standard deviations are equal. Compare it with an appropriate chi-square percentile and state your conclusions.
(c) Calculate the log likelihood ratio test statistic for equality of the three means and of the three standard deviations. Compare it with an appropriate chi-square percentile and state your conclusions.
(d) Tests 1 and 2 employed one type of cord and Test 3 another type. Explain in detail the analyses (fittings and test statistics) you would use to compare the two cord types.
(e*) Use Wald's test to compare the 1 % points of the three distributions, assuming the means and standard deviations may differ.
Table 2.1
