GIVE CORRECT ANSWER WITH DETAILED EXPLANATION:-

Williams College admission Data from 2013 posted on the Williams College website shows that of all 3,195 males applying. 18.2% were admitted, and of all 3,858 females applying. 16.9% were admitted. Let X denote gender of applicant and Y denote whether admitted. a. Which conditional distributions do these percentages refer to, those of Y at given categories of X, or those of X at given categories of Y? Set up a table showing the two conditional distributions. b. Are X and Y independent or dependent? Explain. (Hint: These percentages refer to the population of all applicants in 2013.)Life after death and gender In the 2012 GSS, 605 of 790 males and 822 of 977 females indicated a belief in life after death. (Source: Data from CSM. UC Berkeley.) a. Construct a 2 x 2 contingency table relating gender of respondent (SEX, categories male and female) as the rows to belief about life after death (POSTLIFE, categories yes and no) as the columns. b. Find the four expected cell counts when assuming independence. Compare them to the observed cell counts, identifying cells having more observations than expected. c. For this data, X" = 18.0. Verify this value by plugging into the formula for X" and computing the Sum.\fTesting a genetic theory In an experiment on chlorophyll inheritance in corn, for 1103 seedlings of self-fertilized heterozygous green plants, 854 seedlings were green and 249 were yellow. Theory predicts that 75%% of the seedlings would be green. a. Specify a null hypothesis for testing the theory. b. Find the value of the chi-squared goodness-of-fit statistic and report its of c. Report the P-value, and interpret.\f\fGraduate school information Suppose a liberal arts student is interested in exploring graduate school in his or her field. The student identifies a program in which he or she is interested and finds the name of a few students from that program to interview. In this context, identify what is meant by the (a) subject, (b) sample, and (c) population