7. In Exercise 6 of Chapter 2, data on numbers of publications were given for an SRS of 50 faculty members. Not all departments were represented, however, in the SRS. The SRS contained several faculty members from psychology and from chemistry, but none from foreign languages. The following data are from a stratified sample of faculty, using the areas biological sciences, physical sciences, social sciences, and humanities as the strata. Number of Faculty Members in Sample Stratum Biological Sciences Physical Sciences Social Sciences Humanities Total Number of Faculty Members in Stratum 102 310 217 178 807 7 19 13 11 50 The frequency table for number of publications in the strata is given below. Number of Faculty Members Social Humanities Refereed Publications Biological Physical Number of 820100000 901020100 120121002 12010201O 012345678 (a) Estimate the total number of refereed publications by faculty members in the college, and give the standard error. (b) How does your result from (a) compare with the result from the SRS in Exercise 6 of Chapter 2? (c) Estimate the proportion of faculty with no refereed publications, and give the standard error. (d) Did stratification increase precision in this example? Explain why you think it did or did not.