Probability of Error in Hypothesis Testing

Create a statistical plot illustrating Type I and Type II error probabilities in hypothesis testing. Draw two normal distribution curves on the same axes: one centered at the null hypothesis mean and the other at the alternative hypothesis mean, both with equal standard deviation. Mark a vertical critical line on the right tail of the null distribution, determined by the significance level. Shade three regions: the area under the null curve to the right of the critical line (Type I error), the area under the alternative curve to the left of the critical line (Type II error), and the area under the alternative curve to the right of the critical line (test power). Include sliders to adjust the significance level, standard deviation, null mean, and alternative mean, which dynamically update the curves, critical line, and shaded areas. Display numerical values of these probabilities as text labels that update in real time.