***************************************************************************** * CHAPTER 8 - STATISTICS FOR BUSINESS & ECONOMICS, 4th Ed., by Paul Newbold * ***************************************************************************** * * Example 8.1, page 274 * * 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 90% 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 3 of the Appendix, Fz(1.645)=0.95. * GEN1 LOWER=MEAN-((1.645*SIGMA)/SQRT(N)) GEN1 UPPER=MEAN+((1.645*SIGMA)/SQRT(N)) PRINT LOWER UPPER * DELETE / ALL * *---------------------------------------------------------------------------- * Example 8.2, page 278 * * The random sample of bags of refined sugar is N, the mean is MEAN, and * the standard deviaton is SIGMA. * GEN1 MEAN=19.8 GEN1 N=25 GEN1 SIGMA=1.2 * * The 95% Confidence Interval for the true mean weight for all bags of sugar * produced by the process is calculated with the GEN1 command. The * Lower Bound is defined as LOWER and the Upper Bound is defined as * UPPER. * * Note: From Table 3 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 8.3, page 281 * * The random sample of accounting students is N, the mean is MEAN, and the * standard devation is SIGMA. * GEN1 N=172 GEN1 MEAN=4.38 GEN1 SIGMA=0.70 * * 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 3 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 8.4, page 286 * * The SAMPLE command is used to specify the sample range of data to be read. * The READ command inputs the data and assigns variable names. In this case, * the observation is assigned the variable I and the car fuel consumption * figures in miles per gallon is X. The LIST option on the READ command * lists all data read. * SAMPLE 1 6 READ I X / LIST 1 18.6 2 18.4 3 19.2 4 20.8 5 19.4 6 20.5 * * To replicate the Table at the top of page 287, the GENR command is used * to generate the X-squared. * GENR X2=X**2 PRINT I X X2 * * 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. * STAT X / 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 6 of the Appendix, t=2.015 when n-1=5 and SIGMA/2=0.05. * GEN1 N=6 GEN1 LOWER=MEAN-((2.015*S)/SQRT(N)) GEN1 UPPER=MEAN+((2.015*S)/SQRT(N)) PRINT LOWER UPPER * DELETE / ALL * *---------------------------------------------------------------------------- * Example 8.5, page 288 * * The random sample of merged carriers is N, the mean is MEAN and the * standard deviation is S. * GEN1 N=17 GEN1 MEAN=0.105 GEN1 S=0.440 * * The 95% Confidence Interval for the population mean with a normal population * distribution is calculated with the GEN1 command. The Lower Bound is * defined as LOWER and the Upper Bound is defined as UPPER. * * From Table 6 of the Appendix, t=2.120 when n-1=16 and SIGMA/2=0.025. * GEN1 LOWER=MEAN-((2.120*S)/SQRT(N)) GEN1 UPPER=MEAN+((2.120*S)/SQRT(N)) PRINT LOWER UPPER * DELETE / ALL * *---------------------------------------------------------------------------- * Example 8.6, page 293 * * The random sample of industrial buyers is N and the policy for each * buyer to make his/her own decision or there was no policy on accepting * gifts is defined as PHAT. * GEN1 N=344 GEN1 PHAT=83/N * * The 90% Confidence Interval for the population of all buyers who make * their own decision on accepting gifts from suppliers is calculated with * the GEN1 command. The Lower Bound is defined as LOWER and the Upper * Bound is defined as UPPER. * * From Table 3 of the Appendix, z(0.05)=1.645. * GEN1 LOWER=PHAT-1.645*(SQRT((PHAT*(1-PHAT))/N)) GEN1 UPPER=PHAT+1.645*(SQRT((PHAT*(1-PHAT))/N)) PRINT LOWER UPPER * DELETE / ALL * *---------------------------------------------------------------------------- * Example 8.7, page 294 * * The random sample of company recruiters on college campuses is N and the * grade consideration of a candidate that is "critical", "extremely * important" or "very important" is defined as PHAT. * GEN1 N=142 GEN1 PHAT=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 3 of the Appendix, z(0.025)=1.96. * GEN1 LOWER=PHAT-1.96*(SQRT((PHAT*(1-PHAT))/N)) GEN1 UPPER=PHAT+1.96*(SQRT((PHAT*(1-PHAT))/N)) PRINT LOWER UPPER * DELETE / ALL * *---------------------------------------------------------------------------- * Example 8.8, page 298 * * A random sample of pills for headaches relief is N and the standard * deviation is S. The variance (S2) is the standard deviation squared. * GEN1 N=15 GEN1 S=0.8 GEN1 S2=S**2 * * The 90% Confidence Interval for the population variance for the headache * pills is calculated with the GEN1 command. The Lower Bound is defined * as LOWER and the Upper Bound is defined as UPPER. * * From Table 5 of the Appendix, Chi-squared (14,0.05)=23.68 and * Chi-squared (14, 0.95)=6.57. * GEN1 LOWER=((N-1)*S2/23.68) GEN1 UPPER=((N-1)*S2/6.57) PRINT LOWER UPPER * * Square-root of the LOWER and UPPER bounds must be calculated to determine * the 90% Confidence Interval for the population standard deviation in the * percentage concentration of the active ingredient in the pills. * GEN1 NEWLOW=SQRT(LOWER) GEN1 NEWUP=SQRT(UPPER) PRINT NEWLOW NEWUP * DELETE / ALL * *---------------------------------------------------------------------------- * Example 8.9, page 304 * * The random sample of employees who are smokers is defined as SMOKE, the * mean amount of short-term absenteeism per month from work is SMEAN, and the * standard deviation per month is SSTD. * GEN1 SMOKE=96 GEN1 SMEAN=2.15 GEN1 SSTD=2.09 * * The independent random sample of employees who never smoked is NSMOKE, the * mean amount of absenteeism per month from work is NSMEAN, and the standard * deviation per month is NSSTD. * GEN1 NSMOKE=206 GEN1 NSMEAN=1.69 GEN1 NSSTD=1.91 * * The 99% Confidence Interval for the differenc 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=(SMEAN-NSMEAN)-2.575*(SQRT(((SSTD**2)/SMOKE)+((NSSTD**2)/NSMOKE))) GEN1 UPPER=(SMEAN-NSMEAN)+2.575*(SQRT(((SSTD**2)/SMOKE)+((NSSTD**2)/NSMOKE))) PRINT LOWER UPPER * DELETE / ALL * *---------------------------------------------------------------------------- * Example 8.10, page 305 * * The random sample of professors is PROF, the mean rating is PMEAN, and * the standard deviation is PSTD. * GEN1 PROF=321 GEN1 PMEAN=3.01 GEN1 PSTD=1.09 * * The independent random sample of chief executive officers is CEO, the * mean rating is CMEAN, and the standard deviation per month is CSTD. * GEN1 CEO=94 GEN1 CMEAN=2.88 GEN1 CSTD=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=(PMEAN-CMEAN)-1.96*(SQRT(((PSTD**2)/PROF)+((CSTD**2)/CEO))) GEN1 UPPER=(PMEAN-CMEAN)+1.96*(SQRT(((PSTD**2)/PROF)+((CSTD**2)/CEO))) PRINT LOWER UPPER * DELETE / ALL * *---------------------------------------------------------------------------- * Example 8.11, page 308 * * The random sample of Partial Formal Planners is PFP, the mean annual * percentage increase in net income is PFPMEAN, and the standard deviation * is PFPSTD. * GEN1 PFP=6 GEN1 PFPMEAN=9.972 GEN1 PFPSTD=7.470 * * The independent random sample of banks with no formal planning system is * NFP, the mean annual percentage increase in net income is NFPMEAN, and * the standard deviation is NFPSTD. * GEN1 NFP=9 GEN1 NFPMEAN=2.098 GEN1 NFPSTD=10.834 * * The common population variance (S2) is calculated using the GEN1 command. * GEN1 S2=(((PFP-1)*PFPSTD**2)+((NFP-1)*NFPSTD**2))/(PFP+NFP-2) * * The standard deviation (S) of the common population is the square-root * of the variance. * GEN1 S=SQRT(S2) PRINT S2 S * * The 90% Confidence Interval for the difference between the population mean * percentage increases in net income is calculated with the GEN1 command. * The Lower Bound is defined as LOWER and the Upper Bound is defined as * UPPER. * * From Table 6 of the Appendix, t(13,0.05)=1.771. * GEN1 LOWER=(PFPMEAN-NFPMEAN)-((1.771*S)*(SQRT((PFP+NFP)/(PFP*NFP)))) GEN1 UPPER=(PFPMEAN-NFPMEAN)+((1.771*S)*(SQRT((PFP+NFP)/(PFP*NFP)))) PRINT LOWER UPPER * DELETE / ALL * *---------------------------------------------------------------------------- * Example 8.12, page 310 * * The survey of client-sponsored projects (CSPs) users in schools accrediated * by the American Assembly of Collegiate Schools of Business is ACCRED and * the number of response in these schools who agreed that "CSPs are too * time-consuming for faculty" is ACCAGR. An independent sample of CSP users * in nonaccredited schools is NONACCR and the number that agreed with the * response is NONACCAG. * GEN1 ACCRED=92 GEN1 ACCAGR=49 GEN1 PHATACC=ACCAGR/ACCRED PRINT ACCRED ACCAGR PHATACC GEN1 NONACCR=86 GEN1 NONACCAG=36 GEN1 PHATNON=NONACCAG/NONACCR PRINT NONACCR NONACCAG PHATNON * * The 90% 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=(PHATACC-PHATNON)-1.645*SQRT(((PHATACC*(1-PHATACC))/ACCRED)+& ((PHATNON*(1-PHATNON))/NONACCR)) GEN1 UPPER=(PHATACC-PHATNON)+1.645*SQRT(((PHATACC*(1-PHATACC))/ACCRED)+& ((PHATNON*(1-PHATNON))/NONACCR)) PRINT LOWER UPPER * DELETE / ALL * *---------------------------------------------------------------------------- * Example 8.13, page 311 * * The random sample of male senior accounting students is MALE and the number * of these men expected to be working full time ten years later is MALEFT. * The independent random sample of female senior account students is FEMALE * and the number of these women expected to be working full time ten years * later is FEMALEFT. * GEN1 MALE=120 GEN1 MALEFT=107 GEN1 PHATMEN=MALEFT/MALE PRINT MALE MALEFT PHATMEN GEN1 FEMALE=141 GEN1 FEMALEFT=73 GEN1 PHATWOM=FEMALEFT/FEMALE PRINT FEMALE FEMALEFT PHATWOM * * 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=(PHATMEN-PHATWOM)-1.96*SQRT(((PHATMEN*(1-PHATMEN))/MALE)+& ((PHATWOM*(1-PHATWOM))/FEMALE)) GEN1 UPPER=(PHATMEN-PHATWOM)+1.96*SQRT(((PHATMEN*(1-PHATMEN))/MALE)+& ((PHATWOM*(1-PHATWOM))/FEMALE)) PRINT LOWER UPPER * DELETE / ALL * *---------------------------------------------------------------------------- * Example 8.14, page 315 * * 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 L=0.50 GEN1 SIGMA=1.8 GEN1 Z005=2.575 GEN1 N=((Z005**2)*(SIGMA**2))/(L**2) PRINT N * *---------------------------------------------------------------------------- * Example 8.15, page 317 * * The sample size required to achieve a 95% Confidence Interval for the * proportion of company recruiters who viewed grades 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 L=0.06 GEN1 Z025=1.96 GEN1 N=(0.25*Z025**2)/L**2 PRINT N * DELETE / ALL * *---------------------------------------------------------------------------- STOP