A sociologist randomly selects 372 females 15 to 19 years old and asks each to disclose her family structure at age 14 and whether she has had sexual intercourse. Use the results in the accompanying table to complete parts (a) through below Click here to view the data table of family structure and sexual activity. Click here to view the Chi-Square table of critical values. (a) Compute the expected values of each cell under the assumption of independence. Had sexual intercourse Both Biological or Adoptive Parents Single Parent Parent and Non-parental Guardian Stepparent 42 60 64 31 Yes 53.49 77.32 40.25 25.95 41 82 34 18 No 47.51 68.68 35.75 23.05 (Round to two decimal places as needed.) (b) Verify that the requirements for performing a chi-square test of independence are satisfied. Select all requirements for a chi-square test of independence. YA. No more than 20% of the expected frequencies are less than 5. Data table of family structure and sexual activity YB. All expected frequencies are greater than or equal to 1. OC. All expected frequencies are greater than or equal to 10. Both Biological or Adoptive Parent and Stepparent Non-parental Guardian Single Parent O D. The expected frequencies are approximately Normal. Had sexual intercourse O E. All expected frequencies are greater than or equal to 5. Parents Yes 60 64 42 31 82 34 18 (c) Compute the chi-square test statistic. 41 No X6 = (Round to three decimal places as needed.) %3D Print Done

(0.5,3.4),(0.2,3.7),(1.2,5.5),(2.9,7.3),(3.4,7.9),(2.4,5.9),(4.4,8.1),(4.5,7.9),(4.9,7.9),(3.3,6.6) Compute the coefficients of polynomials of degrees 3,4,5,6,7,8,9(3 to 9) that approximates the above data points in the least-square sense using Cholesky factorization.

Let A = [1,2,3,4; 0,0,1,-1; 2,0,0,-3;1,2,2,5] Determine the rank of A.

A biologist is examining two genetic mutations. Genetic mutation A occurs in 15% of the population, mutation B occurs in 4% of the population, and 1% of the population have mutation B and do not have mutation A. a) Is having mutation A independent of having mutation B? Explain/show the reasoning for your answer. b) Is not having mutation A independent of having mutation B? Explain/show the reasoning for your work.