TI-83 Graphing Calculator Manual for
David S. Moore's
The Basic Practice of Statistics

This page contains the programs that are used in the TI-83 companion manual to The Basic Practice of Statistics by David S. Moore(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 overall sample mean, the pooled sample deviation, the mean square for groups MSG, the mean square for error MSE, the degrees of freedom, the F statistic, and the P-value of the ANOVA test for equality of means when 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.

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.

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].

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.

CONTRLX.83p - Computes and displays the centerline and the upper and lower control limits for an xbar control chart upon entering the sample size and target values of the mean and standard deviation. If the values of xbar from various samples are first stored in list L1, then press GRAPH after executing the program to see the control chart.

CORRTEST.83p -Computes the t test statistic and P-value for testing the hypothesis that the correlation equals 0 based on the sample size and sample correlation.

DIFPCI.83p - Computes a "plus four" 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 plus four estimate for the difference in proportions and the confidence interval.

FITTEST.83p - Performs a test of fit for a specified discrete distribution. Before executing, enter the specified proportions into list L1 and enter the observed cell counts into list L2. The expected cell counts are computed and stored in list L3, and the individual contributions to the chi-square test statistic are stored in list L4. The program displays the test statistic and the P-value.

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.

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

PCONFINT.83p - Computes a "plus four" 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 plus four estimate of the proportion and the confidence interval.

PSAMPSZE.83p - When finding a 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 or 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.

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.

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.

TSCORE.83p - Finds the critical value t* of a t-distribution upon specifying the degrees of freedom and either the probability to the left of t*, to the right of t*, or in between -t* and t*.

TWOTCI.83p - Finds the (Option 2) confidence interval for the difference in means where the critical value t* is obtained from the t distribution having degrees of freedom that is the smaller of n1 - 1 and n2 - 1.

TWOTTEST.83p - Finds the (Option 2) P -value for hypothesis tests about the difference in means where the critical value used is from the t distribution having degrees of freedom that is the smaller of n1 - 1 and n2 - 1.

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.

ZSCORE.83p - Displays the critical value z-score of the standard normal distribution, rounded to the common three decimal places, after the desired confidence level is entered.