\f9) According to the Census Bureau, the distribution by ethnic background of the New York City population in a recent year was Hispanic: 28% B | a c k: 24% White: 35% Asian: 12% Dthe rs: 1% The manager of a large housing complex in the city wonders whether the distribution by race of the oomplex's residents is consistent with the population distribution. To find out, she records data from random sample of SDI] residents. The table below displays the sample data. Race Hispanic Bla ck White Asian Others Count 212 202 270 94 22 Are these data signicantly different from the city's distribution by race? Carry out an appropriate test at the a : 0.05 level of signicance to support your answer. [Use Algebra rst then Tech next] a. State the null and alternate hypotheses (write it mathematically] andwrite your claim. {2 Points] b. Find the letstalistics. [3 Points] c. Identify the Rejection region (critical region) and tail to reject region. Show this by drawing a curve and separate the rejection region from the fail to reject region using the critical value. [3 Points] d. DeCide whether to reject or fail to reject the null. {2 Points] e. Make an interpretation of your decision inthe context. (2 Points] 10] Is achieving a basic skill level related to the location otthe school? The results ofa random sample of students by the location of school and the number of students achieving basic skill level in three subjects is shown in the contingency table. At a : 0.05, answer the following: Subject Location Reading Math Science Urban 4U 49 41 Suburban EU 55 68 [The two categorical variables here are Subject and Location with two and three Categories respectively] [Use Algebra first then Tech next] a. State the null and altemale hypotheses {write it mathematically] and write your claim. (2 points] b. Find the standardizedtest statistic [ 3 Points] c. Decide whether to reject or tail to reject the null. (2 Points] d. Make an interpretation ofyourdecision inthe context. (2 Points]