A hоspitаl аdministrаtоr wants tо optimize staffing levels in the Emergency Department. They want to know if patient arrivals are distributed evenly across the three main nursing shifts, morning, afternoon, and night. They track 450 arrivals over a week and find 132 morning arrivals, 175 afternoon arrivals, and 143 night arrivals. Are patient arrivals uniformly distributed across all three shifts? Sketch a well-labeled side-by-side bar graph that shows both the observed and the expected values for each category of the variable. Use graph paper, if possible. Show all the steps of the Chi-Square goodness of fit test: the null and alternate hypotheses, show the calculations to compute the test statistic, find the P-value (or the critical value), state the decision and explain why that is the correct decision (based either on the P-value or the critical value at the 0.05 level of significance), and write a conclusion in the context of the problem. In other words, explain what the results mean about the distribution of the categorical variable.