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Random sample of size n=19 is taken from a Normal population, sample mean is 11.5895, standard...

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Basic Math

Random sample of size n=19 is taken from a Normal population,sample mean is 11.5895, standard deviation is 1.0883.

1. At the 2% level, test whether it is reasonable to believethat the true population variance is larger than 1.

Using the scenario from above, do the following

2. Derive the power function. Show your work.
3. Using R, graph the power function for 0.5 < sigma^2 <3.5.
4. Pretend that the sample size was actually 56. Plot this powerfunction on the same graph.
5. Based on the power functions graphed in c, why is the testdescribed in part c "better" than the original test? Explain youranswer using the power functions.

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