could you help giving me explanations on this problems :-
Beliefs of college freshmen Every year, a large-scale poll of college freshmen conducted by the Higher Education Research Institute at UCLA asks their opinions about a variety of issues. In 2004, although women were more likely to rate their time management skills as "above average, they were also twice as likely as men to indicate that they frequently feel overwhelmed by all they have to do (36.4% versus 16.3%). a. If results for the population of college freshmen were similar to these, would gender and feelings of being overwhelmed be independent or dependent? b. Give an example of hypothetical population percentages for which these variables would be independent.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.)Sample evidence about independence Refer to the exercise 1. Go to the GSS Web site and construct a table relating happiness (HAPPY) to the variable you chose (AFTERLIF, FINRELA. HEALTH, REGION, or JOBSAT). Inspect the conditional distributions and indicate whether independence seems plausible, with the sample conditional distributions all being quite similar. Exercise 1 What is independent of happiness? Which one of the following variables would you think most likely to be independent of happiness: belief in an afterlife, family income, quality of health, region of the country in which you live, satisfaction with job? Explain the basis of your reasoning.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.Marital happiness and income In Exercise 11.5 when you used the GSS to download a 3 x 3 table for family income and marital happiness in 2012, you should have obtained results similar to the following table. Marital Happiness Income Not Pretty Very Above 62 139 Average 125 283 Below 6 69 115 a. State the null and alternative hypotheses for the test. b. What is the number of degrees of freedom for the chi-squared test? C. The chi-squared statistic for the table equals X" = 4.58. (@) What value do you expect for X if the null hypothesis were true? (ii) How many standard deviations is 4.58 from this expected V2 x df). (mi) Is X
