Texas Instruments TI-83 Plus Manual

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[Page 1] Texas Instruments TI-83 Plus

TI-83, TI-83 Plus and the TI-84 GRAPHING CALCULATOR MANUAL James A. Condor Manatee Community College to accompany Introductory Statistics Sixth Edition by Prem S. Mann Eastern Connecticut State University ...

[Page 2] Texas Instruments TI-83 Plus

Contents Preface 3 1 Introduction 4 2 Organizing Data 11 3 Numerical Descriptive Measures 17 4 Probability 27 5 Discrete Random Variables 32 6 Continuous Random Variables 39 7 Sampling Distributions 46 8 Estimation of the ...

[Page 3] Texas Instruments TI-83 Plus

Preface Statistics is an important field of study, now more so than ever. We are surrounded by statistical information in work and in our everyday lives. Many of us work in professions that require us to understand statistical summaries, and ...

[Page 4] Texas Instruments TI-83 Plus

Chapter 1 Introduction Use of Technology Statistics is a field that deals with sets of data. After the data is collected it needs to be organized and interpreted. There is a limit to how much of the work can be done effectively without th...

[Page 5] Texas Instruments TI-83 Plus

Advantages to Using the TI-83, TI-83 Plus, and TI-84 Plus This calculator manual will focus on how to get the most out of using the TI-83, TI-83 Plus, and the TI-84 Plus calculators by Texas Instruments. The TI-83 was first released in 1996, impr...

[Page 6] Texas Instruments TI-83 Plus

Press the STAT key. To input data or to make changes to an existing set of data values use the Edit function. (number one under the EDIT list). Press the number 1 key...

[Page 7] Texas Instruments TI-83 Plus

Use the up and down arrow keys to go back and forth between the numbers. Try changing the value of one of the entries by typing in a new weight. Clearing a List of Data Values After a list of data values is no longer needed you can delete t...

[Page 8] Texas Instruments TI-83 Plus

You can also store data to a name that you create. From the home screen, you can save a list to a name by using the STO► key. {131, 114, 167, 180, 126, 134, 188, 175, 133, 130} → WEIGH If you type in WEIGH on the home screen and press the...

[Page 9] Texas Instruments TI-83 Plus

LIST menu, and choose one of the list names there by using the arrow keys and then press the ENTER key. In general, when you need to supply the name of a list to a command or a menu, use the LIST page and the NAMES list. Choosing Lists to Ed...

[Page 10] Texas Instruments TI-83 Plus

Exercises 1. Store the following numbers into the list L2: 11, 23, 35, 47, 59 2. Store the following numbers into the list ABC: 2, 3, 5, 7, 11, 13 3. Configure the Stat List Editor to display lists L2, ABC, and L5. 4. Save the ...

[Page 11] Texas Instruments TI-83 Plus

Chapter 2 Organizing Data After the data has been input into the calculator one of the tasks of the statistician is to try to make sense of that data by organizing it. As a consumer of statistics, you are presented with tables and graphical...

[Page 12] Texas Instruments TI-83 Plus

Team Home Runs Team Home Runs Anaheim 152 Milwaukee 139 Arizona 165 Minnesota 167 Atlanta 164 Montreal 162 Baltimore 165 New York Mets 160 Boston 177 New York Yankees 223 Chicago Cubs 200 Oakland 205 Chicago White Sox 217 Philad...

[Page 13] Texas Instruments TI-83 Plus

Press the GRAPH key. Press the TRACE key. Use the arrow keys to move from one bar to the other. (this will supply information on the frequency in each category and the range of values in each category). The histogram provides ...

[Page 14] Texas Instruments TI-83 Plus

We’re going to construct a frequency histogram from the data. The data ranges from 15.4 to 31.2 so we will have our classes go from 15 to 33. That is a range of 33 − 15 = 18, so we will construct six classes of width 3. Go into the Stat List...

[Page 15] Texas Instruments TI-83 Plus

Creating a Dotplot You can create a Dotplot by using the scatterplot option under STATPLOT. The steps to create the dotplot are very similar to those needed to create the histogram. We will use the data stored under the label WORK that we used...

[Page 16] Texas Instruments TI-83 Plus

Exercises 1. Take the following statistics exam scores and construct a frequency histogram for them with classes from 50 to 59, from 60 to 69, from 70 to 79, from 80 to 89, and from 90 to 99. 95 80 76 87 67 83 ...

[Page 17] Texas Instruments TI-83 Plus

Chapter 3 Numerical Descriptive Measures After data is collected and organized the next step is usually to generate descriptive statistics. Descriptive statistics helps you describe the contents of the data set. The two most common measur...

[Page 18] Texas Instruments TI-83 Plus

Example: Prices of CDs. The following data values are the prices of the same popular CD sold from ten different discount stores. 12.95, 14.90, 11.57, 14.65, 17.95, 21.25, 12.95, 20.35, 10.95, 25.05 Press the STAT key. Press the number 1 k...

[Page 19] Texas Instruments TI-83 Plus

The last five numbers (minimum, first quartile, median, third quartile, and maximum) are collectively known as the five-number summary of the data. From the five-number-summary we can compute the range, which is the difference between maxX and minX...

[Page 20] Texas Instruments TI-83 Plus

The first line displays the sample mean, Ë = 78 million dollars. The fourth line displays the sample standard deviation, Sx = 34.4 million dollars. Use the down arrow key to see that the median payroll is 75 million dollars. The interquartile rang...

[Page 21] Texas Instruments TI-83 Plus

Grouped Data Sometimes a set of data values has many numbers that show up over and over again. Instead of typing those numbers in over and over again you can save time by typing in the numbers that repeat along with how many times it repeats. ...

[Page 22] Texas Instruments TI-83 Plus

Press the STAT key. Press the number 1 key. Enter the times in L1. Enter the frequencies in L2. Press the STAT key. Press the ► key to Highlight CALC. Press the ENTER key. Type in L1, L2. Press the ENTER key. ...

[Page 23] Texas Instruments TI-83 Plus

Elementary Statistics Final Exam Scores 76 88 94 73 81 90 62 94 56 71 77 85 76 60 84 73 Enter the exam scores into a list with the name FINAL. Press the STAT key. Press the number 1 key. Press the ▲ key to highlight L1. Pr...

[Page 24] Texas Instruments TI-83 Plus

Box-and-Whisker Plot The TI-83, TI-83 Plus, and TI-84 Plus calculators will take a list of data and automatically draw a box-and-whisker plot for that data. Since there are a number of different types of plots available on the calculator, it is ...

[Page 25] Texas Instruments TI-83 Plus

Set the Freq: to 1. Press the ZOOM key. Press the number 9 key. We have two different types of box-and-whisker plots to select from. One will separate outliers from the maximum or minimum value and the other will include the outliers...

[Page 26] Texas Instruments TI-83 Plus

Exercises 1. Find the mean and sample standard deviation for the following data: 34 23 55 91 23 34 12 34 98 23 2. Find the median and interquartile range for the following grouped data: Score Frequency 34 9 27 11 84 4...

[Page 27] Texas Instruments TI-83 Plus

Chapter 4 Probability Generating Random Numbers When working with probabilities, it is sometimes useful to generate numbers that you can’t predict, but at the same time follow some standard rules. Computer simulations are a common exam...

[Page 28] Texas Instruments TI-83 Plus

Press the ENTER key. Press the ENTER key again. If you continue to press the ENTER key you will generate a different random number between zero and one each time you press the ENTER key. Generating Random Numbers Between any Two Value...

[Page 29] Texas Instruments TI-83 Plus

After the randInt( function appears on your screen you can type in the minimum and maximum values for the range of random numbers you are searching for. The minimum value goes first followed by a comma and then the maximum value. For this exam...

[Page 30] Texas Instruments TI-83 Plus

The syntax for these functions are similar to those needed for the randInt( function. For example, if you wanted to generate 30 numbers from a normal distribution with a mean of 45 and a standard deviation of 8 and store them in L2 you would se...

[Page 31] Texas Instruments TI-83 Plus

Exercises 1. Create a random integer value between 50 and 60 inclusive. 2. Create a random real number between 3 and 17. 3. Generate 15 random integer values between 1 and 50 and store them in L1. 4. Select 10 values from a normally...

[Page 32] Texas Instruments TI-83 Plus

Chapter 5 Discrete Random Variables and Their Probability Distributions Mean and Standard Deviation of a Discrete Random Variable Computing the mean and standard deviation of a discrete random variable is slightly different than ...

[Page 33] Texas Instruments TI-83 Plus

Press the STAT key. Press the number 1 key. Enter the x values into L1. Enter the P(x) probabilities into L2. Press the STAT key. Press the ► key to highlight CALC. Press the number 1 key When 1-Var Stats appears on the c...

[Page 34] Texas Instruments TI-83 Plus

Permutations Another common function needed to compute dependent probabilities that uses factorial is the permutation formula. The number of permutations is normally written as nPr; on the calculator with the symbol P written between n and r, w...

[Page 35] Texas Instruments TI-83 Plus

Binomial Probabilities The command for computing binomial probabilities is binompdf( , which is located on the DISTR page (which is found in yellow above the fourth key in the fourth row). To find the probability of x successes out of n trial...

[Page 36] Texas Instruments TI-83 Plus

Find the probability that at most 2 or less of these 10 packages will not arrive at its destination within the specified time. Press the 2 nd key and then press the VARS key to get to the DISTR page. Press the ALPHA key and then pr...

[Page 37] Texas Instruments TI-83 Plus

Example: New Bank Accounts Suppose that on the average two new accounts per day are opened at an Imperial Savings Branch bank. Let’s find the probability that on a given day at least 7 new accounts are opened. The complement of opening at leas...

[Page 38] Texas Instruments TI-83 Plus

Exercises 1. Find 13! 2. Find the number of ways to deal a five-card hand from a deck of 52 cards. 3. Find the number of four-digit numbers that don’t have any digits repeated. 4. A company has 50 fork-lifts. On any given day each f...

[Page 39] Texas Instruments TI-83 Plus

Chapter 6 Continuous Random Variables and the Normal Distribution Continuous random variables are used to approximate probabilities where there are many possibilities or an infinite number of possibilities on a given trial. One of the mo...

[Page 40] Texas Instruments TI-83 Plus

Press the 2 nd key and then the VARS key to get to the DISTR page. Press the number 1 key. Type in 1, 0, 1) to get normalpdf(1,0,1). Press the ENTER to get .242. To find the probability of getting a value that...

[Page 41] Texas Instruments TI-83 Plus

Press the number 2 key. Type in the number -1. Press the 2 nd key and then the , (comma) key to get the exponential sign E. Type in 99, 0, 1) after the E. Press the ENTER key. The probability is .159. Example: Finding the...

[Page 42] Texas Instruments TI-83 Plus

Example: Finding the Area Between two values. To find the area between two numbers a and b, type normalcdf(a, b, 0, 1). Find the probability of getting a value between 1.04 and 1.82 on the standard normal distribution. Press the 2 nd ke...

[Page 43] Texas Instruments TI-83 Plus

Find the probability of getting a score less than 32 given the distribution is normally distributed with a mean of 45 and a standard deviation of 12. Using the normalcdf( function and typing in -1E99, then the score 32 with a mean of 45 an...

[Page 44] Texas Instruments TI-83 Plus

To find the score that is associated with the lowest 1% of the area under the normal distribution we use invNorm( . Press the 2 nd key and then the VARS key to get to the DISTR page. Press the number 3 key. Type in .01, 54...

[Page 45] Texas Instruments TI-83 Plus

Exercises 1. What is the probability that a z-score will lie between 2 and 3? 2. How likely is it for a z-score to be over 2.5? 3. What is the chance that a z-score is less than 1.3? 4. The heights in inches at a certain age are norma...

[Page 46] Texas Instruments TI-83 Plus

Chapter 7 Sampling Distributions A large part of statistics consists of analyzing the probability of getting a sample mean or sample proportion from a repeated number of samples drawn from the same population. Usually we focus on two kind...

[Page 47] Texas Instruments TI-83 Plus

Press the 2 nd key and then press the VARS key to get to the DISTR page. Press the number 2 key. Type in -1E99, 31.8, 32, .3/ 20 )) Press the ENTER key. The probability is .0014. Example: Tuition According...

[Page 48] Texas Instruments TI-83 Plus

Probabilities for Sample Proportions For a large sample size, we know from the Central Limit Theorem that the sampling distribution for ê is normally distributed with µ ê = p and σ ê = npq/ To find the probability that a < ê < ...

[Page 49] Texas Instruments TI-83 Plus

Exercises 1. Assume that the average annual family income in a given city is $28,000 with standard deviation $3200. If a random sample of fifty families is taken, what is the chance that the average income of the fifty familie...

[Page 50] Texas Instruments TI-83 Plus

Chapter 8 Estimation of the Mean and Proportion In statistics we collect samples to find things out about a population. If the sample is representative of the population, the sample mean or proportion should be statistically close to the ...

[Page 51] Texas Instruments TI-83 Plus

Press the STAT key. Press the ► twice to highlight TESTS. Press the number 7 key. The first line under ZInterval has two options for Inpt: Data Stats. If the mean and standard deviation are given in the problem then Stats should be ...

[Page 52] Texas Instruments TI-83 Plus

We do not have the population standard deviation σ, so we will use TInterval. Press the STAT key. Press the ► key twice to highlight TESTS. Press the number 8 key. We do not have the data itself, so we will select Stats. We en...

[Page 53] Texas Instruments TI-83 Plus

Example: Legal Advice According to a 2002 survey by FundLaw, 20% of Americans needed legal advice during the past year to resolve such thorny issues as trusts and landlord disputes. Suppose a recent sample of 1000 adult Americans showed that 20...

[Page 54] Texas Instruments TI-83 Plus

Exercises 1. Given that σ = 4 for a given population and the following sample data, find a 95% confidence interval for µ. 24 31 31 34 18 22 2. Find a 90% confidence interval for µ given the following sample data f...

[Page 55] Texas Instruments TI-83 Plus

Chapter 9 Hypothesis Tests About the Mean and Proportion Hypothesis Tests About Means Hypothesis tests about means can be Z-based (if σ is known) or T-based (if σ is unknown and either the population is normal or the sample size is over 3...

[Page 56] Texas Instruments TI-83 Plus

Press the STAT key. Press the ► key twice to highlight TESTS. Press the number 2 key. Move the cursor over Stats and press the ENTER key. Type in 50352 for µ 0. Type in 51750 for Ë. Type in 5240 for Sx. Type in 200 for n. Move ...

[Page 57] Texas Instruments TI-83 Plus

Press the STAT key. Press the ► key twice to highlight TESTS. Press the number 2 key. Move the cursor over Stats and press the ENTER key. Type in 65 for µ 0. Type in 63 for Ë. Type in 2 for Sx. Type in 15 for n. Move the cursor...

[Page 58] Texas Instruments TI-83 Plus

defective chips. Test at the 5% significance level whether or not the machine needs an adjustment. Our hypotheses are H 0 : p = 4% and H 1 : p > 4%. We will use 1-PropZTest, with p 0 = 0.04, x = 14, n = 200, and p 1 > p 0 for our altern...

[Page 59] Texas Instruments TI-83 Plus

Press the STAT key. Press the ► key twice to highlight TESTS. Press the number 5 key. Type in .9 for p 0. Type in 129 for x. Type in 150 for n. Move the cursor over <P 0 and press the ENTER key. Move the cursor over Calculate ...

[Page 60] Texas Instruments TI-83 Plus

Exercises 1. Test at a 5% significance level whether or not µ = 98 given the following sample data from a normal population: 97 105 90 89 112 130 2. Test at a 5% significance level whether or not p is more t...

[Page 61] Texas Instruments TI-83 Plus

Chapter 10 Estimation and Hypothesis Testing: Two Populations Confidence Interval for µ1 − µ2 If you are fortunate enough to have information about the population standard deviations, you can use 2-SampZInt to estimate the difference ...

[Page 62] Texas Instruments TI-83 Plus

Press the STAT key. Press the ► key twice to highlight TESTS. Press the number 9 key. Move the cursor over Stats and press the ENTER key. Type in 9000 for σ1 . Type in 8500 for σ2. Type in 49056 for Ë1. Type in 500 for n1. Typ...

[Page 63] Texas Instruments TI-83 Plus

Example: Average Salaries Test at the 1% significance level if the 2001 mean salaries of full-time state employees in New York and Massachusetts are different. We are testing to choose between H 0 : µ1 = µ2 and H 1 : µ1 ø µ2. Since we hav...

[Page 64] Texas Instruments TI-83 Plus

Pretest/Posttest. Data is collected from a sample before some type of treatment and then data is collected again from that same sample after the treatment. We then work with the mean difference between the pre and posttest scores. The null hypot...

[Page 65] Texas Instruments TI-83 Plus

The T-Test output shows the: alternative hypothesis: µ>0 test statistic: t=1.226498265 p-value: p=.1329778401 sample mean: Ë=5 sample standard deviation: Sx=10.78579312 sample size: n=7 The p-value ...

[Page 66] Texas Instruments TI-83 Plus

Enter in the data for the 2-PropZTest. Highlight Calculate and press the ENTER key. The test statistics is 1.15 and the p-value is .13. Since the p-value is larger than the significance level of 1% we accept the null hypothesis. ...

[Page 67] Texas Instruments TI-83 Plus

Exercises 1. Given the following sample data from two populations, find a 95% confidence interval for µ 1 − µ 2 : Ë 1 = 23.5 Ë 2 = 17.9 s 1 = 5.1 s 2 = 2.4 n 1 = 38 n 2 = 59 2. Given the following pa...

[Page 68] Texas Instruments TI-83 Plus

Solutions 1. Since we do not have the population standard deviations, we will use a T-based confidence interval, 2-SampTInt, and select Stats. We enter the sample statistics and choose No for the Pooled pr...

[Page 69] Texas Instruments TI-83 Plus

Chapter 11 Chi-Square Tests Contingency Tables When you are measuring the relationship between two categorical variables, one of the most important tools for analyzing the results is a two-way frequency table. We can use the table to see i...

[Page 70] Texas Instruments TI-83 Plus

Test at a 5% significance level whether or not Gender and Opinion are independent. Then check the expected frequencies for any possible practical significant differences between the associated observed and expected frequencies. First the data...

[Page 71] Texas Instruments TI-83 Plus

Since the p-value of .016 is less than the significance level of .05 we reject the null hypothesis that row and column variables are independent. We have evidence that gender does influence opinions concerning school discipline. The see the exp...

[Page 72] Texas Instruments TI-83 Plus

After MATRIX [A] type in 2 x2. The 2 represents the number of rows in the table. The 2 represents the number of columns in the table. Press the ENTER key. Enter the data values into the matrix as they appear in the table. ...

[Page 73] Texas Instruments TI-83 Plus

Exercises 1. Test at a 5% significance level whether or not state and blood type are independent of each other using the following sample data. Type O Type A Type B Type AB New York 50 40 35 10 California 125 100 120 3...

[Page 74] Texas Instruments TI-83 Plus

Chapter 12 Analysis of Variance One-Way Analysis of Variance We have already seen how to test for the equality of means between two different populations with 2-SampZTest and 2-SampTTest. With the added assumption of common population s...

[Page 75] Texas Instruments TI-83 Plus

Press the STAT key. Press the ENTER key to get to the Stat Editor. Enter the Method I data values into L1. Enter the Method II data values into L2. Enter the Method III data values into L3. Press the STAT key. Press the ► key twice to...

[Page 76] Texas Instruments TI-83 Plus

Teller A Teller B Teller C Teller D 19 14 11 24 21 16 14 19 26 14 21 21 24 13 13 26 18 17 16 20 13 18 At a 5% level of significance, test the null hypothesis that the mean number of customers served per hour by each of the four tellers is ...

[Page 77] Texas Instruments TI-83 Plus

Exercises 1. Test at a 5% significance level whether or not these samples come from populations with identical means. Assume that the populations are all normally distributed with identical standard deviations. A B C...

[Page 78] Texas Instruments TI-83 Plus

Chapter 13 Simple Linear Regression Simple Linear Regression Models A simple linear regression model is an equation describing how to use one variable x to predict another y, based on the relationship that we see in sample data. Since w...

[Page 79] Texas Instruments TI-83 Plus

Press the STAT key. Press the number 1 key. Type the English scores in L1 Type the Math scores in L2. Press the 2 nd key and then the Y= key to get to STATPLOT. Press the number 1 key. Turn Plot1 On and highlight the scatterplot under Ty...

[Page 80] Texas Instruments TI-83 Plus

Press the STAT key. Press the ► key. Press the number 8 key. Press the 2 nd key and then the number 1 key to get L1. Press the , (comma) key. Press the 2 nd key and then the number 2 key to get L2. Press the , (comma) key. Pre...

[Page 81] Texas Instruments TI-83 Plus

Hypothesis Tests Just because we can compute a regression model does not mean that it is a valid model. We can test whether or not the variable x can meaningfully predict the variable y by running LinRegTTest to test whether or not B, the popula...

[Page 82] Texas Instruments TI-83 Plus

Type in L1, L2, Y1. Press the ENTER key. The LinReg output shows the: general model: y=a+bx y-intercept: a=1.142245989 slope: b=.264171123 coefficient of determination: r 2 =.9190178504 linear correlation c...

[Page 83] Texas Instruments TI-83 Plus

Exercises Use the following sample data for the exercises in this chapter. Height (in) 67 71 62 66 74 64 72 74 Weight (lbs) 195 220 100 168 225 130 180 190 1. Compute a regression model for this data and also find the coefficient...

[Page 84] Texas Instruments TI-83 Plus

Chapter 14 Nonparametric Methods Sign Test The Sign Test is one of the most direct nonparametric methods; knowing nothing about the distribution, we can still test claims about the median of a population because any sample measurement...

[Page 85] Texas Instruments TI-83 Plus

Home Price 1 147,500 2 123,600 3 139,000 4 168,200 5 129,450 6 132,400 7 156,400 8 188,210 9 198,425 10 215,300 Using a 5% significance level, can we conclude that the median price differs from $137,000? Our hypotheses are H0 : the m...

[Page 86] Texas Instruments TI-83 Plus

Our hypotheses are H0 : the median is at least $70 versus H1 : the median is less than $70. For a large sample size (n = 89 households that were above or below $70) we can use 1-PropZTest. The p-value is 0.084, which is greater than our significa...

[Page 87] Texas Instruments TI-83 Plus

Since the p-value is less than our significance level 2.5%, we reject the null hypothesis. The data leads us to conclude that the diet does lower the median systolic blood pressure of adults. Example: Math Anxiety Many students suffer from mat...

[Page 88] Texas Instruments TI-83 Plus

Index 1-Var Stats, 13 analysis of variance, 65 ANOVA, 65 binomial distribution, 28 binomial probabilities, 28 box-and-whisker plot, 20 Central Limit Theorem, 39 combinations, 28 confidence interval, 43 confidence interval for µ, 43 confid...

[Page 89] Texas Instruments TI-83 Plus

minimum, 14 naming lists, 4 nonparametric methods, 75 normal distribution, 34 normal probabilities, 34 numbers, pseudo-random, 23 numbers, random, 23 observed frequencies, 59 percentiles, 19 plot, box-and-whisker, 20 Poisson distribution, 3...