The precision of equipment and instruments is measured by the variability of their operation under repeated conditions. The output from an automatic lathe producing the diameter (in millimeters) of a part gave the following readings for a random sample of size 10:

(a) Find a 90% confidence interval for the variance of the diameters.
(b) Find a 90% confidence interval for the standard deviation of the diameters.
(c) Test the null hypothesis that variance of the diameters does not exceed 0.05 mm. Use a significance level of 0.10.
(d) Does the mean setting for the machine need adjustment? Is it significantly different from 9.5 mm? Test at a significance level of 0.10.

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10.3 9.7 9.6 9.5 9.9 10.2 9.8 10. 10.2 9.8