Please solve the following questions

Exercise 1 {33 marks = 4 + is + 5 + at In a certain area, the population consists of four ethnic groups (A, B. C, and D) in the following proportions: Ethnic group A B C D Population proportion 0.13 0.05 0.03 0.?4 A random survey of 1,000 persons in the area employed in managerial and professional positions gives the following results: Ethnic grou p A B C D Observed frequencies 145 45 1'5 1'35 Do these data indicate that the ethnic-group composition of managers and professionals in the area is different from the ethnicgroup composition of the area's population? Let a = [1.05. {a} What is the variable of interest? IS it qualitative or quantitative? If it is qualitative, is it ranked or unranlted? If it is quantitative, is it discrete or continuous? What is its level of measurement? Explain your answers. {it} Answer the research question by performing all necessary calculations manually. State the hypotheses. the decision rule, calculate the test Statistic showing the details of your calculations, make a statistical decision with reference to the proper critical value and draw your conclusion. Based on the relevant clitical value table, what can you tell about the ,o-value ofyourtest'? Explain your answer. {c} Repeat the test you performed in part to} with R. Evaluate the test using the reported pvalue this time. to] List all requirements that must be met to validate the test in parts ([1) and (c). Are they likely satisfied this time? Explain your answers