I'm wondering if you can help with #3, I found that you had helped with 1&2 for a classmate.

Group Work #2: Stratified Random Sampling: 100 Points 1. A university has 807 faculty members. For each faculty member, the number of refereed publications was recorded. A frequency table for number of refereed publications is given below for a simple random sample of 50 faculty members. Refereed Publications Faculty Members 0 28 1 4 2 3 3 4 4 4 5 2 6 1 7 0 8 2 9 1 10 1 a. Estimate the mean number of refereed publications by faculty members in the university, , and place a bound on the error of estimation, B. b. Estimate the total number of refereed publications by faculty members in the university, r, and place a bound on the error of estimation, B. c. Estimate the proportion, p, of faculty with no publications and place a bound on the error of estimation, B. 2. Above, data on numbers of refereed publications were given for a simple random sample of 50 faculty members. Not all departments were represented, however, in the simple random sample. The following data are from a stratified random sample of faculty members, using biological sciences, physical sciences, social sciences, and humanities as the strata. Stratum Members in Stratum Biological Sciences Physical Sciences Social Sciences Humanities Total Number of Faculty 102 310 217 178 807 Number of Faculty Members in Sample 7 19 13 11 50 The frequency distribution for number of publications in the strata is given below. Number Publications 0 1 2 3 4 5 6 7 8 Biological Sciences 1 2 0 1 0 2 0 1 0 Physical Sciences 10 2 0 1 2 1 1 0 2 Social Sciences 9 0 1 0 2 0 1 0 0 Humanities 8 2 0 1 0 0 0 0 0 a. Estimate the total number of refereed publications by faculty members in the university, r, and place a bound on the error of estimation, B. b. How does your estimate for question #2.a compare with the result from the simple random sample in question #1.b? c. Estimate the proportion, p, of faculty with no publications and place a bound on the error of estimation, B. d. Did stratification in question #2.c increase precision relative to your estimate for question #1.c? Explain why you think it did or did not. 3. You have been asked by the university to estimate the average number of publications per faculty member. NOTE: Use the information for question #2 for stratum sizes (use the first table in question #2) and to estimate the stratum standard deviations (use the second table in question #2) for the problems below. a. Determine the total sample size necessary to estimate the mean number of publications, , per faculty member with a bound on the error of estimation, B, of 1.00, and the necessary stratum sample sizes using equal allocation. b. Determine the total sample size necessary to estimate the mean number of publications, , per faculty member with a bound on the error of estimation, B, of 1.00, and the necessary stratum samples sizes using proportional allocation. c. Determine the total sample size necessary to estimate the mean number of publications, , per faculty member with a bound on the error of estimation, B, of 1.00, and the necessary stratum sizes using Neyman allocation. I ' ' " CourseHero|MyQuesh X rd H X/ H https'ww'courseherc X ' D Sampling-Designand X \\H ' ' W - ome' . .Course Hero|VIerue: X \\H Microsoft 0 C I 9 Secure I htlpsi/wwwcoursehero.com/qa,laachmentf2775941.r' : n: hefme w apmoxiumiom m to use the from aprevimls ckplll'hnenl m estimate 07173, .. ., a}, uuwludgc of the lungs of [he obsen'aduws wnrlu'n cuch ysheu's Lheurem aud mm "mm! distlltlulu. me rang: :unuld hr mughiy 46 SD. Mulhuds ut'chunsing lhBlmEli