COURSE SYLLABUS: STAT 1241(2240)

                APPLIED SAMPLING

                TH 9:30-10:45 PM

                 

                 

      Instructor:     Henry W. Block

                   Department of Statistics

                   2703 CL

                   Phone: 624-8369

                   email: hwb@stat.pitt.edu

                 

      Office Hours:  TH 1:15-2:15 PM or by appointment

 

     Grader: Seo Hyon Baik (shb6@pitt.edu), 2504 CL

       

      Grader's Office Hours: Monday, 12 Noon to 2 PM 

   

      Required Text: Schaefer, Mendenhall and Ott Elementary Survey

                 Sampling

     WEbsite: www.stat.pitt.edu/hwb/s1241/

     

      Prerequisite:   STAT 1000 OR STAT 0200 (grade B- or better) including

                        familiarity with MINITAB

     

      Description:    This is an undergraduate course on sample

              surveys and is also appropriate for graduate

              students in departments other than statistics. It

              focuses on various methods of statistical sampling

              encountered in business, the social sciences

              and natural resource management.

              Statistical packages will be used throughout the

              course: MINITAB at first and perhaps SAS later (no

              familiarity is assumed with SAS).

             

     Course Requirements and Grading:

    

              1) 2 Tests    40%

              2) Homeworks   20%

              3) Final      40%

 

     Test #1: Thursday, February 7, Open book (your text) and open notes (notes and HWs).

              Test will cover Chapters 2 through 4. 

 

     Test #2: Thursday, March 27, Open book and notes (as for Test #1).

              Test will cover Chapters 5 and 7.

 

      Final Exam: Wednesday, April 23, 8:00-9:50 AM. Open book and notes as on the midterms.

              Final will cover Chapters 1 - 8.

 

     Homework Assignments:

 

     Number    Date    Assignment

       -       1/10    2.5, 2.16, 2.20, 2.23, 2.28

       1       1/17    3,13 3.14 3.15 3.16 3.18 3.22(grads only)

       2       1/24    3.20 (Take 20 samples of size 5), 4.1, 4.2, 4.6, 4.11

       3       1/31    4.14 4.15 4.16 4.17 4.18.4.40

       4       2/12    4.20 4.21 4.22 4.23 4.24

       5       2/14    5.6 5.8

       6       2/21    5.1 5.2 5.7 5.10 5.11

       7       2/28    5.13 5.14 5.15 5.25 (Grad students only) 5.30(Undergrads only)5.32 

       8       3/6     7.1 7.3 7.6

       9       3/20    7.4 7.5 7.7 7.11 7.12 7.21

      10       4/3     8.1 8.2 8.3 8.4 8.5 

      11       4/10    8.14 8.15 8.17 8.19 8.31 8.32

 

     Macros

        mvarcalm

        mvarcalp

        srsmean

        stallocm

        stallocp

        STMEAN

        stprop

        stsampsm

        stsampsp

        varcalm

        varcalp

       

    

STAT 1241/2240 Homework 7 Solution

By Seo Hyon Baik

 

 

5.13

 

MTB > Execute "C:\Program Files\Minitab 15\English\Macros\stallocp.mtb" 1.

Executing from file: C:\Program Files\Minitab 15\English\Macros\stallocp.mtb

Input the number of strata.

DATA> 4

Input the population size for each stratum.

DATA> 97 43 145 68

Input the population proportion for each stratum.

DATA> 0.9 0.9 0.5 0.5

Input the cost of obtaining an observation from each stratum.

DATA> 4 4 8 8

Input the actual number desired for D.

DATA> 0.000625

The allocations for each stratum are given below:

 

Data Display

 

C36

   0.248067   0.109968   0.437018   0.204946

 

 

The approximate sample size required to estimate p

with a bound B on the error of estimation is

 

Data Display

 

K43    157.203 ≈ 158

 

 

The approximate individual sample sizes for each

stratum are given below:

 

Data Display

 

C37

   38.9970   17.2873   68.7007   32.2182 ≈ 39 17 69 33

 

 

 

5.14

 

The following table lists the sample size, population

size, sample proportion, estimated variance of the

sample proportion, estimated standard deviation of

the sample proportion and the bound on the error of

estimation for each stratum:

 

 

Data Display

 

Row  samsize  popsize  samprop   variance    std dev     bound

  1       39       97     0.87  0.0017797  0.0421859  0.084372

  2       17       43     0.93  0.0024602  0.0496001  0.099200

  3       69      145     0.60  0.0018499  0.0430104  0.086021

4       33       68     0.53  0.0040067  0.0632982  0.126596

 

The estimator of the proportion, where stratified sampling is used is

 

Data Display

 

K9    0.700907

 

 

The estimated variance of the proportion, using stratified sampling is

 

Data Display

 

K13    0.000631692

 

 

The estimated standard deviation of the proportion, using stratified

sampling is

 

Data Display

 

K14    0.0251335

 

 

The bound on the error of estimation, using stratified sampling is

 

Data Display

 

K15    0.0502670

 

 

5.15

 

 

 

 

5.25

 

From (5.7),

 

5.30

 

MTB > Execute "C:\Program Files\Minitab 15\English\Macros\stprop.mtb" 1.

Executing from file: C:\Program Files\Minitab 15\English\Macros\stprop.mtb

MTB > #

MTB > Exec 'mvarcalp'

Executing from file: mvarcalp.MTB

MTB > #

Input the number of strata.

DATA> 2

Executing from file: varcalp.MTB

Input the sample size followed by the population size.

DATA> 100 300

Input the sample proportion.

DATA> 0.7

The sample size is

 

Data Display

 

K11    100.000

 

 

The population size is

 

Data Display

 

K22    300.000

 

 

 

(a)

 

The sample proportion is

 

Data Display

 

K1    0.700000

 

 

The estimated variance of the sample proportion is

 

Data Display

 

K2    0.00141414

 

 

The estimated standard deviation of the sample proportion is

 

Data Display

 

K3    0.0376051

 

 

The bound on the error of estimation is

 

Data Display

 

K4    0.0752101

 

 

Input the sample size followed by the population size.

DATA> 100 500

Input the sample proportion.

DATA> 0.66

The sample size is

 

Data Display

 

K11    100.000

 

 

The population size is

 

Data Display

 

K22    500.000

 

 

The sample proportion is

 

Data Display

 

K1    0.660000

 

 

The estimated variance of the sample proportion is

 

Data Display

 

K2    0.00181333

 

 

The estimated standard deviation of the sample proportion is

 

Data Display

 

K3    0.0425833

 

 

The bound on the error of estimation is

 

Data Display

 

K4    0.0851665

 

 

 

The following table lists the sample size, population

size, sample proportion, estimated variance of the

sample proportion, estimated standard deviation of

the sample proportion and the bound on the error of

estimation for each stratum:

 

 

Data Display

 

Row  samsize  popsize  samprop   variance    std dev      bound

  1      100      300     0.70  0.0014141  0.0376051  0.0752101

  2      100      500     0.66  0.0018133  0.0425833  0.0851665

 

 

(b)

 

The estimator of the proportion, where stratified sampling is used is

 

Data Display

 

K9    0.675000

 

 

The estimated variance of the proportion, using stratified sampling is

 

Data Display

 

K13    0.000907197

 

 

The estimated standard deviation of the proportion, using stratified

sampling is

 

Data Display

 

K14    0.0301197

 

 

The bound on the error of estimation, using stratified sampling is

 

Data Display

 

K15    0.0602394

 

(c)

 

The following table lists the sample size, population

size, sample proportion, estimated variance of the

sample proportion, estimated standard deviation of

the sample proportion and the bound on the error of

estimation for each stratum:

 

 

Data Display

 

Row  samsize  popsize  samprop   variance   std dev     bound

  1       20      300    0.350  0.0111754  0.105714  0.211428

  2       70      500    0.286  0.0025452  0.050449  0.100899

 

MTB >

MTB >

The estimator of the proportion, where stratified sampling is used is

 

Data Display

 

K9    0.310000

 

 

The estimated variance of the proportion, using stratified sampling is

 

Data Display

 

K13    0.00256575

 

 

The estimated standard deviation of the proportion, using stratified

sampling is

 

Data Display

 

K14    0.0506532

 

 

The bound on the error of estimation, using stratified sampling is

 

Data Display

 

K15    0.101306

 

 

Thus,

 

 

 

 

(d)

 

 

(e)

 

 

 

5.32

 

(a)

 

 

> 0.5*7.63+0.1*7.74+0.4*6.55

[1] 7.209

> 

> 2*sqrt((0.5*0.15)^2/1347+(0.1*0.35)^2/163+(0.4*0.11)^2/1095)

[1] 0.00733739

 

 

(b)

95% CIs for the difference between anesthesiology resident and the other are;

 

Since both intervals do not include zero inside and both bounds are positive, it seems that residents have a significantly higher average than the other two groups.

 

STAT 1241/2240 Homework 11 Solution

By Seo Hyon Baik

 

Note: You should correct the dataset 8.14 provided to get the answers in 8.14 and 8.15. The dataset contains the typing errors on 5th and 39th observations.

 

8.14

 

 

 

8.15

 

8.17

8.19

 

Note: ’s are the variances of   which can not be calculated by

 

8.31

 

8.32