***************************************************************************** * CHAPTER 18 - STATISTICS FOR BUSINESS & ECONOMICS, 5th Edition * ***************************************************************************** * Example 18.1, page 708 * * The GEN1 command is used to generate the constants in calculating the 95% * Confidence Interval. * GEN1 BN=1118 GEN1 LN=60 GEN1 XBAR=87300 GEN1 S=19200 GEN1 SIGMA2=(S**2/LN)*((BN-LN)/BN) GEN1 SIGMA=SQRT(SIGMA2) * * The Lower and Upper bounds of the 95% Confidence Interval for the mean * amount of all mortgages taken out in this city last year is calculated * using the GEN1 command. * GEN1 LOWER=XBAR-1.96*SIGMA GEN1 UPPER=XBAR+1.96*SIGMA * * The PRINT command is prints out the results for the constants specified. * PRINT SIGMA2 SIGMA LOWER UPPER * DELETE / ALL *----------------------------------------------------------------------------- * Example 18.2, page 709 * * The GEN1 command is used to generate the constants in calculating the 99% * Confidence Interval. * GEN1 BN=1395 GEN1 LN=400 GEN1 XBAR=320.8 GEN1 S=149.7 GEN1 NXBAR=BN*XBAR GEN1 BNSIGMA2=((S**2/LN)*BN)*(BN-LN) GEN1 BNSIGMA=SQRT(BNSIGMA2) * * The Lower and Upper bounds of the 99% Confidence Interval for the population * total is calculated using the GEN1 command. * GEN1 LOWER=NXBAR-2.575*BNSIGMA GEN1 UPPER=NXBAR+2.575*BNSIGMA PRINT NXBAR BNSIGMA2 BNSIGMA LOWER UPPER * DELETE / ALL *----------------------------------------------------------------------------- * Example 18.3, page 711 * * The GEN1 command is used to generate the constants in calculating the 90% * Confidence Interval. * GEN1 BN=1395 GEN1 LN=400 GEN1 P=141/LN GEN1 SIGMA2=(P*(1-P)/(LN-1))*((BN-LN)/BN) GEN1 SIGMA=SQRT(SIGMA2) * * The Lower and Upper bounds of the 90% Confidence Interval for the percentage * of all colleges in which business statistics is a two-semester course is * calculated using the GEN1 command. * GEN1 LOWER=P-1.645*SIGMA GEN1 UPPER=P+1.645*SIGMA PRINT P SIGMA2 SIGMA LOWER UPPER * DELETE / ALL *----------------------------------------------------------------------------- * Example 18.4, page 715 * * The GEN1 command is used to generate the constants in calculating the 95% * Confidence Interval. * GEN1 X1BAR=21.2 GEN1 S1=12.8 GEN1 X2BAR=13.3 GEN1 S2=11.4 GEN1 X3BAR=26.1 GEN1 S3=9.2 GEN1 BN1=60 GEN1 LN1=12 GEN1 BN2=50 GEN1 LN2=10 GEN1 BN3=45 GEN1 LN3=9 GEN1 BN=155 GEN1 LN=31 * * Population mean estimate XSTBAR. * GEN1 XSTBAR=((BN1*X1BAR)+(BN2*X2BAR)+(BN3*X3BAR))/BN PRINT XSTBAR * * Estimated mean number of weekly orders per restaurant is: * GEN1 SIGMAX12=(S1**2/LN1)*((BN1-LN1)/BN1) GEN1 SIGMAX22=(S2**2/LN2)*((BN2-LN2)/BN2) GEN1 SIGMAX32=(S3**2/LN3)*((BN3-LN3)/BN3) PRINT SIGMAX12 SIGMAX22 SIGMAX32 * * An ampersand, &, is used at the end of the line to be continued. SHAZAM * will remove the & from the equation and put the two pieces together. Any * space typed before the ampersand will be retained in the equation. The * maximum length of a command including continuation lines is 4096 characters. * GEN1 SIGXST2=(((BN1**2)*SIGMAX12)+((BN2**2)*SIGMAX22)+((BN3**2)*SIGMAX32))/& BN**2 GEN1 SIGMAXST=SQRT(SIGXST2) * * The Lower and Upper bounds of the 95% Confidence Interval for the mean * number of orders per restaurant received in a week is: * GEN1 LOWER=XSTBAR-1.96*SIGMAXST GEN1 UPPER=XSTBAR+1.96*SIGMAXST PRINT SIGXST2 SIGMAXST LOWER UPPER * DELETE / ALL *----------------------------------------------------------------------------- * Example 18.5, page 717 * GEN1 BN1=364 GEN1 BN2=1031 GEN1 LN1=40 GEN1 LN2=60 GEN1 X1BAR=154.3 GEN1 X2BAR=411.8 GEN1 S1=87.3 GEN1 S2=219.9 * * Population total estimate is: * GEN1 NXSTBAR=(BN1*X1BAR)+(BN2*X2BAR) PRINT NXSTBAR * * Total number of students in business courses estimate is: * GEN1 SIGX12=((S1**2)/LN1)*((BN1-LN1)/BN1) GEN1 SIGX22=((S2**2)/LN2)*((BN2-LN2)/BN2) GEN1 N2SIGXST=((BN1**2)*SIGX12)+((BN2**2)*SIGX22) GEN1 NSIGXST=SQRT(N2SIGXST) PRINT SIGX12 SIGX22 N2SIGXST NSIGXST * * The Upper and Lower bounds of the 95% Confidence Interval for the estimated * total number of students in business statistics courses is: * GEN1 LOWER=NXSTBAR-1.96*NSIGXST GEN1 UPPER=NXSTBAR+1.96*NSIGXST PRINT LOWER UPPER * DELETE / ALL *----------------------------------------------------------------------------- * Example 18.6, page 718 * GEN1 BN1=364 GEN1 BN2=1031 GEN1 LN1=40 GEN1 LN2=60 GEN1 P1=7/40 GEN1 P2=13/60 * * Population proportion estimate is: * GEN1 PST=((BN1*P1)+(BN2*P2))/(BN1+BN2) * * The quantities are: * GEN1 SIGP1=((P1*(1-P1))/(LN1-1))*((BN1-LN1)/BN1) GEN1 SIGP2=((P2*(1-P2))/(LN2-1))*((BN2-LN2)/BN2) PRINT PST SIGP1 SIGP2 GEN1 SIGPST2=(((BN1**2)*SIGP1)+((BN2**2)*SIGP2))/(BN1+BN2)**2 GEN1 SIGPST=SQRT(SIGPST2) PRINT SIGPST2 SIGPST * * The Lower and Upper bounds of the 90% Confidence Interval for the proportion * of all colleges in which this course is taught in the economics department * is: * GEN1 LOWER=PST-1.645*SIGPST GEN1 UPPER=PST+1.645*SIGPST PRINT LOWER UPPER * DELETE / ALL *----------------------------------------------------------------------------- * Example 18.7, page 724 * * The required sample observations needed in Example 18.1 is calculated with * the GEN1 command. * GEN1 N=1118 GEN1 SIGMA=20000 GEN1 SIGXBAR=4000/1.96 * * The required sample size, LN, is: * GEN1 LN=(N*SIGMA**2)/(((N-1)*SIGXBAR**2)+SIGMA**2) PRINT LN * DELETE / ALL * *----------------------------------------------------------------------------- * Example 18.8, page 725 * * The required sample observations needed in Example 18.3 is calculated with * the GEN1 command. * GEN1 N=1395 GEN1 SIGPX=0.04/1.96 * * The required sample observations, NMAX, is: * GEN1 NMAX=(0.25*N)/(((N-1)*(SIGPX**2))+0.25) PRINT NMAX * DELETE / ALL *----------------------------------------------------------------------------- * Example 18.9, page 727 * * The required sample observations need in Example 18.4 is calculated with * the GEN1 command. * GEN1 N1=60 GEN1 N2=50 GEN1 N3=45 GEN1 SIGMA1=13 GEN1 SIGMA2=11 GEN1 SIGMA3=9 GEN1 SIGXST=3/1.96 GEN1 NSIGMA=((N1*SIGMA1**2)+(N2*SIGMA2**2)+(N3*SIGMA3**2)) GEN1 NNSIGMA=((N1*SIGMA1)+(N2*SIGMA2)+(N3*SIGMA3))**2/(N1+N2+N3) * * The sample size needed for proportional allocation is: * GEN1 N=NSIGMA/(((N1+N2+N3)*SIGXST**2)+(NSIGMA/(N1+N2+N3))) PRINT NSIGMA NNSIGMA N * * When the optimal allocation method is used, the sample observation required * is: * GEN1 TOP=(((N1*SIGMA1)+(N2*SIGMA2)+(N3*SIGMA3))**2)/(N1+N2+N3) GEN1 BOT=((N1+N2+N3)*(SIGXST**2))+(NSIGMA/(N1+N2+N3)) GEN1 OPTN=TOP/BOT PRINT OPTN * DELETE / ALL *----------------------------------------------------------------------------- * Example 18.10, page 730 * SAMPLE 1 20 READ(INCCLUST.DIF) / DIF LIST * GEN1 M=1000 GEN1 LM=20 * * The STAT command is used to calculate the total number of households in * the sample. The SUM= option saves the sum of N in the constant SUMN. * STAT N / SUM=SUMN GENR NXBAR=N*INCOME STAT NXBAR / SUM=SNXBAR GENR NP=N*P STAT NP / SUM=SNP PRINT SUMN SNXBAR SNP * * The Point Estimates are: * GEN1 XC=SNXBAR/SUMN GEN1 PC=SNP/SUMN PRINT XC PC * * The average cluster size is calculated with the GEN1 command. * GEN1 NBAR=SUMN/20 PRINT NBAR GENR FRAC=(N**2)*(INCOME-XC)**2 STAT FRAC / SUM=SFRAC GEN1 SIGMA2=((M-LM)/(M*LM*NBAR**2))*(SFRAC/(LM-1)) GEN1 SIGMA=SQRT(SIGMA2) PRINT SIGMA2 SIGMA * * The Lower and Upper bounds of the 95% Confidence Interval for the mean * income of all families in this area is: * GEN1 LOWER=XC-1.96*SIGMA GEN1 UPPER=XC+1.96*SIGMA PRINT LOWER UPPER * * The interval estimate for the population proportion is: * area is * GENR Z=(N**2)*(P-PC)**2 STAT Z / SUM=SZ GEN1 ZZ=SZ/(LM-1) GEN1 SIGMAPC2=((M-LM)/(M*LM*NBAR**2))*ZZ GEN1 SIGMAPC=SQRT(SIGMAPC2) PRINT ZZ SIGMAPC2 SIGMAPC * * The Lower and Upper bounds of the 95% Confidence Interval for the mean * income of all families in this area is: * GEN1 LOWER=PC-1.96*SIGMAPC GEN1 UPPER=PC+1.96*SIGMAPC PRINT LOWER UPPER * DELETE / ALL *----------------------------------------------------------------------------- * Example 18.11, page 733 * * The GEN1 command is used to generate the constants to estimate a population * mean. * GEN1 N=1120 GEN1 MEAN=4 GEN1 SIGMA=30.27 GEN1 SMEAN=4/1.96 * * The total number of sample observations required in this study of 100 * accounts receivable is calculated with the GEN1 command. * GEN1 LN=(N*SIGMA**2)/(((N-1)*SMEAN**2)+SIGMA**2) PRINT LN * DELETE / ALL *----------------------------------------------------------------------------- * Example 18.12, page 733 * * The mean family incomes and sample standard deviations in three stratum * districts in a town are defined using the GEN1 command. * GEN1 N1=1150 GEN1 N2=2120 GEN1 N3=930 * GEN1 STD1=3657 GEN1 STD2=6481 GEN1 STD3=8403 * * The DO-loop is used to repeat operations. In this case, the DO-loop is * used to calculate the proportion of the total sample to be allocated to * each stratum under the optimal scheme. The statements between the DO and * ENDO commands are repeatedly executed. In this example, the statements * are repeated 3 times. * DO #=1,3 GEN1 NN#=(N#*STD#)/((N1*STD1)+(N2*STD2)+(N3*STD3)) PRINT NN# ENDO * * Now the total number of sample observations needs to be determined with * the GEN1 command. The total number of population members is the sum * of the three districts. The GEN1 command is used to calculate this number * and the constant is stored in the variable BN. * GEN1 SIGMAX=500/1.96 GEN1 BN=N1+N2+N3 PRINT SIGMAX BN GEN1 NUMERAT=(1/BN)*((N1*STD1)+(N2*STD2)+(N3*STD3))**2 * * The GEN1 statement for the denominator is too long. An ampersand, &, is * used at the end of the line to be continued. SHAZAM will remove the & * from the equation and put the two pieces together. * GEN1 DENOMIN=(BN*(SIGMAX**2))+((1/BN)*((N1*STD1**2)+(N2*STD2**2)+& (N3*STD3**2))) * * The total number of sample observations is: * GEN1 LN=NUMERAT/DENOMIN PRINT LN * * A DO-loop is used to calculate the sample in each stratum. * DO %=1,3 GEN1 FN%=NN%*LN PRINT FN% ENDO * DELETE / ALL *----------------------------------------------------------------------------- * STOP