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(4)(a)An army recruiting center knows from past experience that the weight of army recruits is normally...

(4)(a)An army recruiting center knows from past experience that the weight of army recruits is normally distributed with a mean, u, of 80 kg. and a standard deviation of 10 kg. The recruiting center wants to test, at the 1% level of significance, if the average weight of this year’s recruits is significantly different from past observations. To do this, it takes a random sample of 25 recruits and finds that the average weight for this sample is 85 kg. Conduct this test and explain your result in the context of the goal of the recruiting center.

(b) Suppose a larger sample of 100 recruits is taken and the mean of this sample is found to be the same as in the previous sample. Would your conclusion be different from what you found in the earlier case? Explain

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