TI-83 Graphing Calculator Manual for
Moore, McCabe, Duckworth, and Sclove's

This page contains the programs that are used in the TI-83 companion manual to The Practice of Business Statistics by Moore, McCabe, Duckworth, and Sclove (W. H. Freeman and Company College Publishing). In this companion manual, problems from each section of the text are worked using either the built-in functions or programs specially written for the TI-83. The unequaled capabilities and usefulness of the TI-83 are demonstrated throughout. It is hoped that all students, teachers, and practitioners of statistics discover and make use of these capabilities. I hope you find the manual to be helpful.

The TI-83 manual was written by David K. Neal, Department of Mathematics, Western Kentucky University, Bowling Green, KY 42101 USA: david.neal@wku.edu.

## Index of Programs

ANOVA1.83p - Displays the pooled deviation, the F statistic, the P-value, and the R-squared coefficient of the ANOVA test for equality of means when the data is entered as summary statistics. Before executing the program, enter the sample sizes into list L1, the sample means into list L2, and the sample deviations into list L3.

ANOVA2.83p - Displays the P-values for two-way analysis of variance. If there is one observation per cell, then enter the data into matrix [A] before executing the program. If there are c observations per cell, then enter the means into matrix [A] and the standard deviations into matrix [B]. Also stores the marginal means for the rows and columns into lists L2 and L4. The overall mean is stored as the first value in list L5. The remainder of L5 are the values SSA, SSB, and SSE.

ANPOWER.83p - Computes the Winer approximation of the power of the ANOVA test for alternative population means. Before executing the program, enter the successive sample sizes into list L1 and the alternative population means into list L2. After entering the level of significance and the guessed standard deviation, the approximate power is displayed along with the values of F*, DFG, DFE, and the noncentrality parameter.

AUTOREG.83p - Computes the simple linear regression coefficients for a first-order autoregression model. Before executing the program, enter time series data into list L1. The program displays the predicted value for the next future time period and stores the regression function in Y1. The settings for a lagged time plot are also adjusted. The plot appears when you press GRAPH.

BAYES.83p - Computes the total probability P(A) and conditional probabilities associated with Bayes' rule. Before executing the program, enter values for P(Bi) into list L1 and the conditionals P(A | Bi) into list L2. The program displays P(A) , stores P(A & Bi) into list L3, stores P(Bi | A) into list L4, stores P(Bi | A') into list L5, and stores P(A | Bi') into list L6.

BINOMIAL.83p - Computes the probability of a binomial distribution upon entering values for n, p, and for the lower and upper bounds. The program displays the probability along with the average value. Has an option to store the entire distribution into lists L1, L2, and L3.

BOOT.83p - Performs resampling on a random sample that is entered into list L1 before executing the program. If a bootstrap confidence interval for the statistic is desired, enter 1 for CONF. INTERVAL?; otherwise, enter 0. The program takes resamples from the entered random sample and enters their means into list L2. The mean of all resamples, the bootstrap standard error, and the confidence interval (if specified) are displayed.

BOOTCORR.83p - Perfoms the bootstrap procedure on the correlation coefficient or the regression slope for paired sample data that is entered into lists L1 and L2. When prompted, enter 1 if you want to bootstrap the correlation coefficient and enter 2 if you want to bootstrap the regression slope. The resampled statistics are stored in list L3. The statistic of the original sample data is displayed along with the bootstrap standard error and the confidence interval.

BOOTNORM.83p - Performs resampling from a specified normally distributed population. The program enters a random sample into list L1, then takes resamples from this sample and enters their means into list L2. The mean of all resamples and the bootstrap standard error are displayed.

BOOTPAIR.83p - Computes a bootstrap t-confidence interval for the difference in means based on random samples that are entered into lists L1 and L2. The resampled differences in mean are stored in list L3. The difference of the original sample averages is displayed along with the bootstrap standard error and the confidence interval.

BOOTTEST.83p - Performs a permutation test for the difference in means. Before executing, enter data from the first population into list L1 and enter data from the second population into list L2. When prompted, enter 1, 2, or 3 to designate the desired alternative. The resampled differences in permuted mean are ordered and then stored in list L3. The program displays the difference in the original sample means and the P-value.

BOOTTRIM.83p - Computes a bootstrap t-confidence interval for a trimmed mean on a random sample that is entered into list L1 before executing the program. Enter the desired number of resamples, the decimal amount to be trimmed at each end, and the desired confidence level. The program takes resamples from the entered random sample and enters their trimmed means into list L2. The trimmed mean of the original sample, the trimmed bootstrap standard error, and the confidence interval are displayed.

BTPRTEST.83p - Performs a permutation test for either the difference in paired means or for the correlation. Before executing, enter the data set into lists L1 and L2. When prompted, enter 1 or 2 to designate the enter desired test, then enter 1, 2, or 3 to designate the desired alternative. The resampled permuted pair differences in mean (or correlations) are ordered and stored in list L3. The statistic from the original paired sample is displayed along with the P-value.

CAPIND.83p - Computes the capability indexes for a control process with specified LSL andUSL. An option exists to enter the mean and standard deviation directly or to specify that sample means and sample deviations are already entered into lists L1 and L2 respectively.

CELLS.83p - Performs the chi-square test on a two-way table of random data that has been entered into matrix [A]. Displays the chi-square test statistic, the P-value, and the degrees of freedom. The expected cell counts are stored in matrix [E] and the components of the chi-square test statistic from each cell are stored in matrix [F].

CONTRAST.83p - Computes the P-value for a significance test and a confidence interval for population contrasts. Before executing the program, enter the sample sizes into list L1, the sample means into list L2, the sample deviations into list L3, and the contrast equation coefficients into list L4. In the program, enter either 1 or 2 for a one-sided or two-sided alternative.

CONTRL.83p - Computes the upper and lower control limits and graphs the control charts for xbar and s. Before executing the program, enter the previously obtained sample means into list L1 and the sample deviations into list L2. For the xbar chart, enter the sample sizes, the desired mean, and the desired standard deviation to receive the control limits. For the s chart, enter the the sample sizes and the desired standard deviation. Press GRAPH to see the chart if the means and deviations have been entered into L1 and L2.

CONTRL2.83p - Computes the control limits and graphs the control charts for xbar and s based on past data. Before executing the program, enter the previously obtained sample means into list L1 and the sample deviations into list L2.

CONTRLP.83p - Computes the control limits for sample proportions. Enter the summary statistics of total successes, number of stages, and number of attempts per stage into the program, or enter the numbers of successes for each stage into list L1 and the numbers of attempts for each stage into list L2 before executing the program. In the second case, press GRAPH to see a control chart after the program executes.

DIFPCI.83p - Computes a Wilson confidence interval for the difference of population proportions upon entering the number of "Yes" responses and sample sizes for each population and the desired level of confidence. The program displays the Wilson estimate for the difference in proportions, its standard error, and the confidence interval.

GEOMET.83p - Computes the probability of a geometric distribution upon entering values for p and for the lower and upper bounds. The program displays the probability along with the median and the average value. Has an option to store the entire distribution into lists L1, L2, and L3.

KRUSKAL.83p - Performs the Kruskal-Wallace test. Before executing, enter the data into the columns of matrix [A] and the sample sizes into a row matrix [B]. If the sample sizes are not all equal, then fill out extra entries in matrix [A] with zeros. The program displays the test statistic and P-value. Then L3 contains the merged, sorted measurements, L4 contains their (averaged) ranks, and L5 contains the sum of ranks from each population.

LOG1.83p - Computes the coefficients of the linear regression model for the log of odds ratio. Also displays the odds ratio.

MOVEAVG.83p - Computes a list of moving averages for time series data. Before executing, enter the time series data into list L1. After the desired span is entered, the program computes the successive moving averages, stores them in list L3, then displays the final average. To see a time plot of the moving averages, press GRAPH.

MULTREG.83p - Computes the regression coefficients, the squared correlation coefficient, an ANOVA table, the F statistic and the P-value for a multiple linear regression model. Before executing the program, enter sample data as columns in matrix [A] with the last column used for the dependent variable. The regression coeffecients are stored into matrix [D] and the ANOVA table is stored in lists L1, L2, and L3.

NORMDIST.83p - Displays the probability of a normal distribution upon entering values for the mean, standard deviation, lower bound, and upper bound. Displays the left and right tail values, and the body area when entering the same value for the lower bound and upper bound.

ODDS.83p - Computes the appropriate mathematical odds for a given probability p of an event A. If p < .50, then the odds against A are given as the ratio (1-p) : p. If p > .50, then the odds in favor of A are given as the ratio p : (1-p).

ODDS2.83p - Computes the odds in favor ratio between two proportions.

ODDSINT.83p - Computes confidence intervals for the logistic regression slope and odds ratio.

ODDSTEST.83p - Computes the test statistic and P-value for the hypothesis test that an odds ratio equals 1.

PCONFINT.83p - Computes a Wilson confidence interval for a population proportion upon entering the number of "Yes" responses, the sample size, and the desired level of confidence. The program displays the Wilson estimate of the proportion, its standard error, and the confidence interval.

POISSON.83p Computes and displays the probability of a Poisson distribution upon entering values of the mean and the lower and upper bounds. Has an option to store the entire distribution in lists L1, L2, and L3.

POWER2T.83p - Computes a standard normal approximation of the power of the two sample t-test upon entering values for the alternative mean difference, the two sample sizes, the level of significance, and the common standard deviation.

PSAMPSZE.83p - When finding a Wilson confidence interval for a proportion, computes the required sample size that would give a maximum margin of error m with a specified level of confidence.

RANDOM.83p - Chooses a random subset of k integers from the set 1 to n. It can also be used to permute the entire set n integers. The program displays the random choices and also stores the values into list L1.

RANKSUM.83p - Performs the Wilcoxon rank sum test on data from two populations. Before executing, enter the data into lists L1 and L2. The program displays the expected sum of ranks from list L1 and the sums of the ranks from each list. It then displays the smallest tail-value created by the test statistic which is the sum of the ranks from L1. After the program runs list L3 will contain the merged, sorted measurements, and L4 will contain their (averaged) ranks.

REG1.83p - Finds confidence intervals for the regression slope and intercept. Before executing the program, data must be entered into lists and the LinRegTTest (from the STAT TESTS menu) must be performed.

REG2.83p - Finds a confidence interval for a mean response and a prediction interval for an estimated response when performing linear regression. Before executing the program, data must be entered into lists and the LinRegTTest (from the STAT TESTS menu) must be performed.

REG3.83p - Computes the ANOVA table for linear regression and displays the associated F-statistic and P-value. Before executing the program, data must be entered into lists L1 and L2. The ANOVA table is stored into lists L4, L5 and L6.

SAMPLEN.83p - Generates a random sample from a specified normal distribution and stores the data into list L1. Then displays the sample mean and sample deviation to compare with the true parameters.

SAMPLEN2.83p - Generates a specified number of random samples, each of the same specified sample size from a specified normal distribution. Also computes the sample mean for each sample and stores it into list L2. Then displays the average and standard deviation of the sample means to compare with theoretical mean and standard deviation of the sampling statistics.

SAMPLEP.83p - Generates count data for a specified proportion p and sample size and stores the data into list L1. Then displays the sample proportion to compare with the true proportion.

SAMPLEP2.83p - Generates a specified number of random samples of count data, each of the same specified sample size and for the same proportion p. Also computes the sample proportion for each sample and stores it into list L2. Then displays the average of the sample proportions to compare with the real proportion.

SIGN.83p - Performs the sign test on paired data. Before executing the program, enter the "Before" measurements into list L1 and the "After" measurements into list L2. The program displays the number of positive changes, the number of changes, and P-value for the specified alternative.

SIGNRANK.83p - Performs the Wilcoxon signed rank test on data sets of size n from two populations. Before executing, enter the data into lists L1 and L2. The program sorts the absolute value of the differences L2 - L1 into list L3, but disregards any zero differences. The (averaged) rank of each non-zero difference is stored in L4. The sums of the ranks of the negative differences and of the positive differences are displayed. The program also displays the smallest tail-value created by the test statistic which is the sum of the ranks of the positive differences.

SMOOTH.83p - Calculates and plots the sequence of forecasts based on the exponential smoothing model. Before executing, enter time series data into list L1, then enter the desired weight to execute the program. The sequence of forecasts are computed and stored in list L2, and the forecast for the next time period is displayed. To see a time plot of the forecasts, press GRAPH.

TPOWER.83p - Computes the power against an alternative for hypothesis tests about the mean when using a known standard deviation and critical t-score values.

TSCORE.83p - Finds the critical value (t score) of a t-distribution upon specifying the degrees of freedom and confidence level.

TWOWAY.83p - Converts a two-way table of raw data into three different proportion tables. Before executing the program, enter the raw data into matrix [A]. The joint distribution is then stored in matrix [B], the conditional distribution on the column variable is stored in [C], and the conditional distribution on the row variable is stored in [D].

UNIFORM.83p - Displays the probability of a uniform distribution upon entering values for the left and right endpoints and for the lower and upper bounds.

ZPOWER.83p - Computes the power against an alternative for hypothesis tests about the mean when using a known standard deviation and normal distribution z-scores.

ZSAMPSZE.83p - Computes the sample size needed to obtain a desired maximum margin of error with a specified level of confidence when finding a confidence interval for the mean using normal distribution z-scores.