An experimenter is interested in the hypothesis testing problem H0 : > 420.0 versus HA : < 420.0 where p is the average

An experimenter is interested in the hypothesis testing problem
H0 : μ > 420.0 versus HA : μ < 420.0
where p is the average radiation level in a research laboratory. Suppose that a sample of n = 29 radiation level measurements is obtained and that the experimenter wishes to use a value of σ = 10.0 for the standard deviation of the radiation levels.
(a) For what values of the z.-statistic does the experimenter1 accept the null hypothesis with a size α =0.10?
(b) For what values of the z-statistic does the experimenter reject the null hypothesis with a size α = 0.01?
Suppose that the sample mean is x- = 415.7.
(c) Is the null hypothesis accepted or rejected with α = 0.10? With α = 0.01?
(d) Calculate the exact p-value.