TI-83 Graphing Calculator Manual for Moore and McCabe's Introduction to the Practice of Statistics

This page contains the programs that are used in the TI-83 companion manual to Introduction to the Practice of Statistics (4th Edition) by Moore and McCabe (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 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.
(Note: The form of the outputs in this program have been modified from the progam in the printed manual. In addition, if there are more than 1 observation per cell, then the program now also displays the F statistic and P-value for the test of there being no interaction in any cell.)

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.

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.

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]. 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.

MULTREG.83p - Computes the regression coefficients, the squared correlation coefficient, an ANOVA table, 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.
(Note: This program has been slightly modified from the program in the printed manual. It now also displays the F test statistic and the regression standard error s.)

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.

ODDSTEST.83p - Computes the test statistic and P-value for an 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.

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.
(Note: The output of the F-statistic and P-value are slightly different in this program than the program in the printed manual.)

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.

TESTNORM.83p - Performs a Chi-square goodness of fit test for normality. Before executing, enter sample data into list L1. For testing, we may specify one, both, or neither of the parameters µ and s. The test statistic and P-value are displayed. The frequencies and expected numbers of occurrences per bin are stored into lists L2 and L3.

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.