Please solve this by hand and also with r-studio code not the excel output please.  An experimenter is interested in the hypothesis testing problem with H0: µ = 420 versus Ha: µ < 420, where µ is the average radiation level in a research laboratory. Suppose that a sample of 49 radiation level measurements is obtained and that the experimenter wishes to use σ=10.0 for the standard deviation of the radiation levels. (a) What is the rejection region when α=0.01? (b) Suppose that the sample mean is 415.7. What would be the experimenter’s decision of the hypothesis test based on the rejection region? (c) What is the p-value for this hypothesis test?

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