*****************************************************************************
* CHAPTER 7 - STATISTICS FOR BUSINESS & ECONOMICS, 5th Edition              *
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* Example 7.1, p. 222
*
* 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 cae, the years of experience for six employees is assigned EXPER.
* The LIST option on the READ command lists all data read.
*
SAMPLE 1 6
READ EXPER / LIST
2
4
6
6
7
8
*
* The STAT command is used to calculate the mean experience of the six
* employees in years on the job.
*
STAT EXPER
*
DELETE / ALL
*----------------------------------------------------------------------------
* Example 7.2, p. 224
*
* The Mean and Standard Deviation of the annual percentage salary increase
* for the CEO of all mid-size corporations is defined as MEANX and SIGMAX.
* The random sample is defined as N.
*
GEN1 MEANX=12.2
GEN1 SIGMAX=3.6
GEN1 N=9
*
* The GEN1 command is used to calculate the standard error of the sampling
* distribution of the sample mean.
*
GEN1 SIGMAMX=SIGMAX/SQRT(N)
PRINT SIGMAMX
*
* The probability that the sample mean will be less than 10% is:
*
GEN1 PZ=(10-MEANX)/SIGMAMX
PRINT PZ
*
* From Table 1 of the Appendix, Fz(1.83)=0.9664
*
GEN1 FZ=0.9664
GEN1 PMEANX=1-FZ
PRINT PMEANX
*
* The above probability PMEANX can be easily calculated in SHAZAM with the 
* the GEN1 and DISTRIB command is used to print out critical values in lieu 
* of referring to a statistical table.  The GEN1 command is used to generate
* a constant, X, at the 1% level of significance before the DISTRIB command
* can be executed.  The format of the DISTRIB command is:
*
*  DISTRIB vars / options
*
*  where:  vars      = list of variables
*          options   = list of desired options
*          TYPE=     - specifies the type of distribution
*          DF=       - specifies the degrees of freedom 
*          INVERSE   = computes the inverse survival function
* 
GEN1 Z=12.2
GEN1 SIG2=1.2**2
DISTRIB Z / TYPE=NORMAL MEAN=10 VAR=SIG2
*
DELETE / ALL
*----------------------------------------------------------------------------
* Example 7.3, p. 225
*
* The mean life of spark plugs is defined as MEANX,  standard deviation is
* SIGMAX, average life is AVGLIF, and the random sample size is N.
*
GEN1 MEANX=36000
GEN1 SIGMAX=4000
GEN1 AVGLIF=34500
GEN1 N=16
GEN1 SIGMAMX=SIGMAX/SQRT(N)
PRINT SIGMAMX
GEN1 PZ=(AVGLIF-MEANX)/SIGMAMX
PRINT PZ
*
GEN1 Z=36000
GEN1 SIG2=1000**2
DISTRIB Z / TYPE=NORMAL MEAN=34500 VAR=SIG2
*
DELETE / ALL
*----------------------------------------------------------------------------
* Example 7.4, 231
*
* The Per Capita Annual Income and its standard deviation is defined as MEAN
* and SIGMA.  The random sample and mean income is defined as N and XBAR.
*
GEN1 MEAN=60000
GEN1 SIGMA=5000
GEN1 N=36
GEN1 XBAR=62300
GEN1 Z=(XBAR-MEAN)/(SIGMA/SQRT(N))
PRINT Z
*
GEN1 P=60000
GEN1 SIG2=(5000/SQRT(36))**2
DISTRIB P / TYPE=NORMAL MEAN=62300 VAR=SIG2
*
DELETE / ALL
*----------------------------------------------------------------------------
* Example 7.5, 231
*
* The mean for the random sample claims, mean level for individual claims,
* standard deviation is defined as N, MEAN and SIGMA.  The 95 percent
* confidence interval for the insurance claim is defined as UPPER for the
* upper bound and LOWER for the lower bound.
*
GEN1 N=100
GEN1 MEAN=4000
GEN1 SIGMA=2000
GEN1 Z95=1.96
GEN1 UPPER=MEAN+Z95*(SIGMA/(SQRT(N)))
GEN1 LOWER=MEAN-Z95*(SIGMA/(SQRT(N)))
PRINT UPPER LOWER
*
DELETE / ALL
*----------------------------------------------------------------------------
* Example 7.6, p. 
*
* Read this example carefully.  Be sure you understand the methodology.
*
*----------------------------------------------------------------------------
* Example 7.7, p.237
*
* The random sample of homes is defined as N and the proportion of homes with
* unsafe wiring is M.
*
GEN1 N=250
GEN1 M=0.30
*
* First calculate the standard error (SIGMAP).
*
GEN1 SIGMAP=SQRT((M*(1-M))/N)
*
* Then the probability that the proportion of homes in the sample with
* unsafe wiring between 0.25 and 0.35 is:
*
GEN1 PL=(0.25-M)/SIGMAP
GEN1 PU=(0.35-M)/SIGMAP
PRINT PL PU
*
GEN1 Z=0.30
GEN1 VAR=0.029**2
DISTRIB Z / TYPE=NORMAL MEAN=0.25 VAR=VAR
GEN1 CDF=$CDF
DISTRIB Z / TYPE=NORMAL MEAN=0.35 VAR=VAR
GEN1 VALUE=CDF-$CDF
PRINT VALUE
*
DELETE / ALL
*----------------------------------------------------------------------------
* Example 7.8, p. 238
*
* The proportion of business graduates who believe a course in business ethics
* is very important is M and the random sample size of business graduates is
* N.
*
GEN1 M=0.43
GEN1 N=80
*
* First calculate the standard error (SIGMAP).
*
GEN1 SIGMAP=SQRT((M*(1-M))/N)
PRINT SIGMAP
*
* Then the probability that more than one-half of the business graduates
* believe that a course in business ethics is very important is:
*
GEN1 M=(0.50-M)/SIGMAP
PRINT M
*
GEN1 Z=0.43
GEN1 VAR=0.055**2
DISTRIB Z / TYPE=NORMAL MEAN=0.50 VAR=VAR
*
DELETE / ALL
*----------------------------------------------------------------------------
* Example 7.9, p. 244
*
* N is the random sample of components, SIGMAX is the standard deviation of
* the components.
*
GEN1 N=6
GEN1 SIGMA=3.6
GEN1 SIGMA2=SIGMA**2
*
* Upper Limit, K is:
*
GEN1 K=(11.07*SIGMA2)/(N-1)
PRINT K
*
GEN1 X=0.05
DISTRIB X / TYPE=CHI DF=5 INVERSE
*
DELETE / ALL
*----------------------------------------------------------------------------
* Example 7.10, p. 244
*
* Read this example carefully.  Be sure you understand the methodology.
*
*----------------------------------------------------------------------------
*
STOP