Insulating fluid. The table below shows estimates of the parameters of the extreme value distributions of In time to breakdown of an insulating fluid at seven voltage stresses. The following analyses assess the equality of the seven extreme value scale parameters (Weibull shape), which are equal according to engineering theory.
(a) Calculate the pooled estimate of the extreme value scale parameter.
(b) Calculate the quadratic test statistic (4.1), using the scale parameter estimates. How many degrees of freedom does i t have? Look up the 90 and 95% points of the corresponding chi-square distribution. Do the
seven estimates differ statistically significantly? I f so, how?
(c) How good is the chi-square approximation?
(d) Calculate the quadratic test statistic (4.1), using the In estimates of the scale parameters and omitting the pooled scale parameter estimate from the denominator of (4.1). How many degrees of freedom does this statistic have? Look up the 90 and 95% points of the corresponding chi-square distribution. Do the seven estimates differ statistically significantly? If so, how?
(e) How good is this chi-square approximation?
( f ) Would you expect the two test statistics to be roughly equal or not? Why?
