*****************************************************************************
* CHAPTER 8 - STATISTICS FOR BUSINESS & ECONOMICS, 5th Edition              *
*****************************************************************************
* Example 8.1, p. 259
*
* Read this example carefully.  Be sure you understand the methodology.
*
*----------------------------------------------------------------------------
* Example 8.2, p. 259
*
* The SAMPLE command is used to specify the sample range of the data to be
* read.  The READ command inputs the data and assigns variable names.  In
* this case, the observation number is assigned I and the price-earning ratio
* of ten stocks traded on the New York Stock Exchange on a particular day
* is assigned X.  The LIST option on the READ command lists all data read.
*
SAMPLE 1 13
READ X / LIST
10
16
13
11
12
14
12
15
14
14
13
13
13
*
* The STAT command automatically prints out the sample mean, variance,
* and standard deviation of the variable specified.  The MEAN= option saves
* the mean of X in the constant SMEAN, the VAR= option saves the variance
* and STDEV= option saves the standard deviation.  The PRINT command is used
* used to print out the saved values.
*
STAT X / MEAN=SMEAN VAR=SVAR STDEV=SSTD 
PRINT SMEAN SVAR SSTD
*
DELETE / ALL
*----------------------------------------------------------------------------
* Example 8.3, p. 264
*
* A random sample observation is defined as N, the standard deviation as
* SIGMA and the mean as MEAN.  The GEN1 command is used to generate these
* constants.
*
GEN1 MEAN=25
GEN1 SIGMA=6
GEN1 N=16
*
* The 95% Confidence Interval for the population mean is calculated with the
* GEN1 command.  The Lower Bound is defined as LOWER and the Upper Bound is
* defined as UPPER.
*
* Note:  From Table 1 of the Appendix, Fz(1.96)=0.975.
*
GEN1 LOWER=MEAN-((1.96*SIGMA)/SQRT(N))
GEN1 UPPER=MEAN+((1.96*SIGMA)/SQRT(N))
PRINT LOWER UPPER
*
DELETE / ALL
*----------------------------------------------------------------------------
* Example 8.4, p. 266
*
* The contents of a random sample of bags of refined sugar is N, the mean is
* MEAN, and the standard devation is SIGMA.
*
GEN1 N=25
GEN1 MEAN=19.8
GEN1 SIGMA=1.2
*
* The 99% Confidence Interval for the population mean is calculated with
* the GEN1 command.  The Lower Bound is defined as LOWER and the Upper
* Bound is defined as UPPER.
*
* Note:  From Table 1 of the Appendix, Fz(2.575)=0.9950
*
GEN1 LOWER=MEAN-((2.575*SIGMA)/SQRT(N))
GEN1 UPPER=MEAN+((2.575*SIGMA)/SQRT(N))
PRINT LOWER UPPER
*
DELETE / ALL
*----------------------------------------------------------------------------
* Example 8.5, p. 272
*
* The SAMPLE command is used to specify the sample range of data to be read.
* The READ command inputs the data.  The DIF option on the READ command
* tells SHAZAM that the file to be read contains information about the
* variable names and number of variables.
*
SAMPLE 1 24
READ(TRUCKS.DIF) / DIF
*
* The sample mean, variance and standard deviation of X is automatically
* calculated with the STAT command.  The MEAN=, VAR= and STDEV= options
* will store the mean, variance and standard deviation as a constant which
* can then be used in constructing the 90% Confidence Interval.
*
PRINT MPG
STAT MPG / MEAN=MEAN VAR=S2 STDEV=S
PRINT MEAN S2 S
*
* The 90% Confidence Interval for the population mean fuel consumption
* assuming the population distribution is normal is calculated with the
* GEN1 command.  The Lower Bound is defined as LOWER and the Upper Bound
* is defined as UPPER.
*
* From Table 8 of the Appendix, t=1.714 when n-1=23 and SIGMA/2=0.05.
*
GEN1 N=24
GEN1 LOWER=MEAN-((1.714*S)/SQRT(N))
GEN1 UPPER=MEAN+((1.714*S)/SQRT(N))
PRINT LOWER UPPER
*
DELETE / ALL
*----------------------------------------------------------------------------
* Example 8.6, p. 276
*
* The random sample of registered voters is N and voters who think that
* the state should have a uniform voting process is defined as P.
*
GEN1 N=344
GEN1 P=261/N
*
* The 90% Confidence Interval for the population proportion of all voters
* who agree with a change to a uniform process is calculated with
* the GEN1 command.  The Lower Bound is defined as LOWER and the Upper
* Bound is defined as UPPER.
*
* From Table 1 of the Appendix, z(0.05)=1.645.
*
GEN1 LOWER=P-1.645*(SQRT((P*(1-P))/N))
GEN1 UPPER=P+1.645*(SQRT((P*(1-P))/N))
PRINT LOWER UPPER
*
DELETE / ALL
*----------------------------------------------------------------------------
* Example 8.7, page 278
*
* The random sample of graduate admissions personnel is N and the proportion
* of graduate admissions personnel that found the standardized test scores
* to be "very important" is defined as PAT.
*
GEN1 N=142
GEN1 P=87/N
*
* The 95% Confidence Interval for the proportion of company recruiters with
* this view is calculated with the GEN1 command.  The Lower Bound is defined
* as LOWER and the Upper Bound is defined as UPPER.
*
* From Table 1 of the Appendix, z(0.025)=1.96.
*
GEN1 LOWER=P-1.96*(SQRT((P*(1-P))/N))
GEN1 UPPER=P+1.96*(SQRT((P*(1-P))/N))
PRINT LOWER UPPER
*
DELETE / ALL
*----------------------------------------------------------------------------
* Example 8.8, p. 282
*
* A random sample of temperatures is N and the variance is S2.  
*
GEN1 N=25
GEN1 S2=100
*
* The 95% Confidence Interval for the population variance temperature is
* calculated with the GEN1 command.  The Lower Bound is defined LOWER and
* the Upper Bound is defined as UPPER.
*
* From Table 7 of the Appendix, Chi-squared (24,0.025)=39.364 and
* Chi-squared (24, 0.975)=12.401.
*
GEN1 LOWER=((N-1)*S2/39.364)
GEN1 UPPER=((N-1)*S2/12.401)
PRINT LOWER UPPER
*
DELETE / ALL
*----------------------------------------------------------------------------
* Example 8.9, p. 285
*
SAMPLE 1 8
READ PAIR A B / LIST
1 29 26
2 32 27
3 31 28
4 32 27
5 32 30
6 29 26
7 31 33
8 30 36
*
* The GEN1 command is used to calculate the Difference, D and the squared
* Difference, D2 for each pair.  The STAT command combined with the MEAN=
* option saves the Sample Mean of the difference and the STD= option saves
* Sample Variance of the differences.
*
GENR D=A-B
GENR D2=D**2
STAT D / MEAN=DBAR STD=SD
PRINT DBAR SD
*
* Replicate Table 8.4B
*
PRINT PAIR A B D D2
*
* The 99% Confidence Interval for the difference between the population
* means is calculated with the GEN1 command.  The Lower Bound is defined as
* LOWER and the Upper Bound is defined as UPPER.
*
* From Table 8 of the Appendix, t=3.499 when n-1=7 and SIGMA/2=0.005
*
GEN1 N=8
GEN1 LOWER=DBAR-((3.499*SD)/SQRT(N))
GEN1 UPPER=DBAR+((3.499*SD)/SQRT(N))
PRINT LOWER UPPER
*
DELETE / ALL
*----------------------------------------------------------------------------
* Example 8.10, p. 287
*
* The independent random sample of information systems professors is IS,
* the mean time ISMEAN, and the standard deviation is ISTD.
*
GEN1 IS=321
GEN1 ISMEAN=3.01
GEN1 ISTD=1.09
*
* The independent random sample of accounting professors is ACC, the
* mean rating is AMEAN, and the standard deviation per month is ASTD.
*
GEN1 ACC=94
GEN1 AMEAN=2.88
GEN1 ASTD=1.01
*
* The 95% Confidence Interval for the difference between the two population
* means is calculated with the GEN1 command.  The Lower Bound is defined as
* LOWER and the Upper Bound is defined as UPPER.
*
GEN1 LOWER=(ISMEAN-AMEAN)-1.96*(SQRT(((ISTD**2)/IS)+((ASTD**2)/ACC)))
GEN1 UPPER=(ISMEAN-AMEAN)+1.96*(SQRT(((ISTD**2)/IS)+((ASTD**2)/ACC)))
PRINT LOWER UPPER
*
DELETE / ALL
*-----------------------------------------------------------------------------
* Example 8.11, p. 289
*
* In this example, the sample sizes of the amounts paid by residents for
* speeding tickets in Orange City and DeLand are not identical.  In Orange
* City, the sample consists of 10 tickets while in DeLand the sample consists
* of 8 tickets.  Therefore, it is necessary to a separate SAMPLE and READ
* commands for each of the cities to read in the data.
*
SAMPLE 1 10
READ ORANGE / LIST
100
125
135
128
140
142
128
137
156
142
*
* The STAT command and MEAN= option is used to save the mean cost of
* speeding tickets in Orange City and the VAR= option saves the sample
* variance.
*
GEN1 NX=10
STAT ORANGE / MEAN=XBAR VAR=SX2
PRINT NX XBAR SX2
SAMPLE 1 8
READ DELAND / LIST
95
87
100
75
110
105
85
95
*
* The STAT command and MEAN= option is used to save the mean cost of
* speeding tickets in DeLand and the VAR= option saves the sample
* variance.
*
GEN1 NY=8
STAT DELAND / MEAN=YBAR VAR=SY2
PRINT NY YBAR SY2
*
* The pooled sample variance is calculated with the GEN1 command.
*
GEN1 SP2=(((NX-1)*SX2)+((NY-1)*SY2))/(NX+NY-2)
PRINT SP2
*
* The 95% Confidence Interval for the difference in the mean cost of
* speeding tickets in these two cities is calculated with the GEN1 command.
* The Lower Bound is defined as LOWER and the Upper Bound is defined as
* UPPER.
*
* From Table 8 of the Appendix, t(16,0.025)=2.12
*
GEN1 LOWER=(XBAR-YBAR)-2.12*SQRT((SP2/NX)+(SP2/NY))
GEN1 UPPER=(XBAR-YBAR)+2.12*SQRT((SP2/NX)+(SP2/NY))
PRINT LOWER UPPER
*
DELETE / ALL
*----------------------------------------------------------------------------
* Example 8.12, 291
*
* The sample mean, size and standard deviation of the accounts payable for
* the East Office is XBAR, NX and SX.  The sample mean, size and standard
* deviation of the accounts payable for the West Office is YBAR, NY and SY.
*
GEN1 XBAR=290
GEN1 NX=16
GEN1 SX=15
GEN1 YBAR=250
GEN1 NY=11
GEN1 SY=50
*
* Calculate the degrees of freedom using the GEN1 command.  The "&" symbol
* is used to tell SHAZAM that the command continues to the next line.

*
GEN1 V=((((SX**2)/NX)+((SY**2)/NY))**2)/((((SX**2)/NX)**2/(NX-1))+(((SY**2)&
/NY)**2/(NY-1)))
PRINT V
*
* The 95% Confidence Interval for the difference between the mean values
* of the accounts payables for the two offices is calculated with the GEN1
* command.  The Lower Bound is defined as LOWER and the Upper Bound is
* defined as UPPER.
*
* From Table 1 of the Appendix, t(12,0.025)=2.179
*
GEN1 LOWER=(XBAR-YBAR)-2.179*(SQRT(((SX**2)/NX)+((SY**2)/NY)))
GEN1 UPPER=(XBAR-YBAR)+2.179*(SQRT(((SX**2)/NX)+((SY**2)/NY)))
PRINT LOWER UPPER
*
DELETE / ALL
*----------------------------------------------------------------------------
* Example 8.13, p. 294
*
* The random sample of registered voters in Precinct A is NA and the number
* in Precinct A that supported the candidate in question is VOTEA.  The
* independent random sample of registered voters in Precinct B is NB and the
* number in Precinct B that supported the candidate in question is VOTEB.
*
GEN1 NA=120
GEN1 VOTEA=107
GEN1 PA=VOTEA/NA
PRINT NA VOTEA PA
GEN1 NB=141
GEN1 VOTEB=73
GEN1 PB=VOTEB/NB
PRINT NB VOTEB PB
*
* The 95% Confidence Interval for the difference between population
* proportions is calculated with the GEN1 command.  The "&" command
* is to continue the GEN1 command onto the following line.  The Lower Bound
* is called LOWER and the Upper Bound is called UPPER.
*
GEN1 LOWER=(PA-PB)-1.96*SQRT(((PA*(1-PA))/NA)+((PB*(1-PB))/NB))
GEN1 UPPER=(PA-PB)+1.96*SQRT(((PA*(1-PA))/NA)+((PB*(1-PB))/NB))
PRINT LOWER UPPER
*
DELETE / ALL
*----------------------------------------------------------------------------
* Example 8.14, p. 297
*
* The sample size required to achieve a 99% Confidence Interval extending no
* further than 0.50 mm on each side of the sample mean is defined as N using
* the GEN1 command.
*
GEN1 B=0.50
GEN1 SIGMA=1.8
GEN1 Z005=2.576
GEN1 N=((Z005**2)*(SIGMA**2))/(B**2)
PRINT N
*
*----------------------------------------------------------------------------
* Example 8.15, p. 299
*
* The sample size required to achieve a 95% Confidence Interval for the
* proportion of graduate admissions personnel recruiters who viewed scores
* on standardized exams as very important in the consideration of a candiate
* extends no further than 0.06 on each side of the sample proportion is
* defined as N using the GEN1 command.
*
GEN1 B=0.06
GEN1 Z025=1.96
GEN1 N=(0.25*Z025**2)/B**2
PRINT N
*
DELETE / ALL
*----------------------------------------------------------------------------
* Example 8.16, p. 300
*
* The sample sized required to achieve a 95% Confidence Interval for the
* number of citizens of voting age need to obtain a 3% margin of error is
* defined as N using the GEN1 command.
*
GEN1 B=0.03
GEN1 Z025=1.96
GEN1 N=(0.25*Z025**2)/B**2
PRINT N
*
DELETE / ALL
*----------------------------------------------------------------------------
STOP