Suppose we are interested in learning about the average crop yield of wheat when adding a new change to the soil conditions. To do so, we formed 25 plots of land and measured the total yield per plot in kg. We will assume that x₁, dots, x₂₅ follow the normal distribution with an unknown mean µ and standard deviation of 1 ton. Suppose we wish to test H₀: µ = 4 tons, and Hₐ: µ >4 tons at level α = 0.05.
(A) Do we need the xᵢ 's to be normally distributed in order to conduct the appropriate hypothesis test in this case? And should we conduct a T or Z test?