For part b) please, thank you!.

4.* (a) Two independent random samples, of m and 712 observations, are drawn from normal distributions with the same variance 02. Let S? and 8% be the sample variances of the rst and the second samples, respectively. Show that: 32 _ (n1 135+W2 053 m + H2 2 is an unbiased estimator of a2. Hint: Remember the expectation of a chisquared variable is its degrees of freedom. Two makes of car safety belts, A and B, have breaking strengths which are normally distributed with the same variance. A random sample of 140 belts of make A and a random sample of 220 belts of make B were tested. The sample means, and the sums of squares about the means (i.e. 21.31:,- :1'3)2), of the breaking strengths (in lbf units) were (2,685, 19,000) for make A, and (2,680, 34,000) for make B, respectively. Is there signicant evidence to support the hypothesis that belts of make A are stronger on average than belts of make B? Assume a 1% signicance level