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1 Bolts are manufactured with a nominal length of 6cm. The technology is well established and the variance of the lengths of such bolts is known to be 0:09cm2 . A random sample of 12 bolts is taken and the measurements of their lengths, in cm, are
5.4 6.3 6.1 5.8 6.2 6.3
5.7 6.2 6.3 6.1 6.0 5.7
(a) Find the following sample statistics of the data: mean, variance, standard deviation, minimum, maximum, median, lower quartile, upper quartile, interquartile range, [11]
(b) find out a 95% con?dence interval for the population mean. [7]
(c) Test, at the level of signi?cance 0.05, the hypothesis that the population variance is indeed 0:09cm2

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