5) In Problem 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. Stratum Biological Sciences Physical Sciences Social Sciences Humanities Total Number of Refereed Publications 0 1 2 3 4 5 6 7 8 Number of Faculty Members in Stratum 1 2 102 310 217 178 0 1 0 807 The frequency table for number of publications in the strata is given below. Number of Faculty Members Biological Physical Social 10 2 0 Number of Faculty Members in Sample 1 2 1 1 0 9 0 1 0 2 0 1 0 0 7 19 13 11 8 2 0 1 0 0 0 0 0 50 Humanities a) Estimate the total number of refereed publications by faculty members in the college, and give the standard error. Note: For a frequency table, Y₁ = Σjesh fnjynj, and sh = -1 Σjesn fnj (Ynj — Yn) ². nh b) How does your result from (a) compare with the result from the SRS in Problem 2? Hint: Compare (i) s's for the individual strata with s² as a whole, and (ii) standard errors. c) Estimate the proportion of faculty with no refereed publications, and give the standard error. Hint: Information about no refereed publications is given in the first row of the frequency table for number of publications d) Use no more than four sentences to explain why the stratified sampling did or did not increase the precision in this example.
5) In Problem 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. Stratum Biological Sciences Physical Sciences Social Sciences Humanities Total Number of Refereed Publications 0 1 2 3 4 5 6 7 8 Number of Faculty Members in Stratum 1 2 102 310 217 178 0 1 0 807 The frequency table for number of publications in the strata is given below. Number of Faculty Members Biological Physical Social 10 2 0 Number of Faculty Members in Sample 1 2 1 1 0 9 0 1 0 2 0 1 0 0 7 19 13 11 8 2 0 1 0 0 0 0 0 50 Humanities a) Estimate the total number of refereed publications by faculty members in the college, and give the standard error. Note: For a frequency table, Y₁ = Σjesh fnjynj, and sh = -1 Σjesn fnj (Ynj — Yn) ². nh b) How does your result from (a) compare with the result from the SRS in Problem 2? Hint: Compare (i) s's for the individual strata with s² as a whole, and (ii) standard errors. c) Estimate the proportion of faculty with no refereed publications, and give the standard error. Hint: Information about no refereed publications is given in the first row of the frequency table for number of publications d) Use no more than four sentences to explain why the stratified sampling did or did not increase the precision in this example.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
Transcribed Image Text:5) In Problem 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.
Stratum
Biological Sciences
Physical Sciences
Social Sciences
Humanities
Total
Number of
Refereed Publications
0
1
2
3
4
5
6
7
8
1
2
0
1
Number of
Faculty Members
in Stratum
2
0
1
0
102
310
217
178
The frequency table for number of publications in the strata is given below.
Number of Faculty Members
Biological Physical Social
807
Refereed Publications
Faculty Members
10
2
0
1
0
28
DIINI
2
=
Note: For a frequency table. Yn = —Σjesh fn¡Ynj, and s½ 2 =
nh
1
4
0
2
Number of
Faculty Members
in Sample
0
1
0
0
0
7
8
2
0
1
931
0
0
0
0
11
a) Estimate the total number of refereed publications by faculty members in the college, and give the
standard error.
50
Humanities
b) How does your result from (a) compare with the result from the SRS in Problem 2?
Hint: Compare (i) s's for the individual strata with s² as a whole, and (ii) standard errors.
c) Estimate the proportion of faculty with no refereed publications, and give the standard error.
Hint: Information about no refereed publications is given in the first row of the frequency table for
number of publications
1
nh-1 Σjesh fnj (Ynj - ÿn)².
d) Use no more than four sentences to explain why the stratified sampling did or did not increase the
precision in this example.
Problem 2.
A university has 807 faculty members. For each faculty member, the number of refereed publications
was recorded. This number is not directly available on the database, so requires the investigator
to examine each record separately. A frequency table for number of refereed publications is given
below for an SRS of 50 faculty members.
2 3 4 56 789 10
3
4
4 2 102 1
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step 1: Write the given information
VIEWStep 2: Estimate the total number of refereed publications by faculty members in the college
VIEWStep 3: Compare result from (a) with the result from the SRS in Problem 2
VIEWStep 4: Estimate the proportion of faculty with no refereed publications, and give the standard error.
VIEWSolution
VIEW
Step by step
Solved in 5 steps with 56 images
Recommended textbooks for you
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman