CALCULATOR INSTRUCTIONS FOR TI 81, 82, 83/84 AND 85 GRAPHICS CALCULATORS

Transcription

1 TI Graphing Calculators APPENDIX Reiland CALCULATOR INSTRUCTIONS FOR TI 81, 8, 83/84 AND 85 GRAPHICS CALCULATORS The calculations necessary to summarize even a relatively small data set can be tedious and time-consuming; however, the focus in this course is not on crunching numbers by mindlessly plugging data into blackbox formulas. The solution of real-world statistical problems involves three parts: (1 identify the appropriate technique, ( compute the required statistics, and (3 interpret the results. Our emphasis is on the first and third parts because calculating the statistics can be done relatively easily with calculators and/or computers. To assist students in focusing on technique and interpretation, in this appendix we provide an introduction to several models of Texas Instruments graphics calculators. These calculators provide powerful hand-held tools for taking the drudgery out of the statistical analysis of data. If you have one of these particular calculators then the instructions can be followed exactly; the instructions will allow you to perform the basic operations presented in this course. You are urged to also study your user's guide; you will find that your calculator can do far more than we can cover in this appendix. If you are using a different calculator, then consult the user's guide for use of the statistical functions. I will provide whatever assistance I can in helping you use the statistical features of your calculator, no matter what type you own. You do not need to purchase a special calculator for this course; the one you have now is probably sufficient. See me if you have questions about the adequacy of your calculator. Basics TI81 TI8 TI85 1. Reset to factory settings (be careful! resetting will erase data and programs # $ & F3 1 F1 F4. Darken (lighten screen ÐfÑ ÐfÑ ÐfÑ ÐfÑ 3. Clear screen CLEAR CLEAR CLEAR CLEAR The reset process erases all stored data, settings, and programs. If you are not saving anything, this routine can be used to clear the calculator before each new problem.

2 page If you want to clear old data from the calculator without changing anything else, the following keystrokes can be used: s TI81 TI8 TI85 Clear the stat data editor; STAT STAT STAT return to blank screen MATRX 4 4 F # 1 1 F5 CLEAR CLEAR CLEAR EXIT Note: For the TI8 and, the instructions above clear data from column L1. To clear columns L1 and L, add just before. Histograms To construct histograms with a TI graphics calculator it is necessary to know the lower boundary of the first class, the upper boundary of the last class, and the class length. We illustrate by constructing a histogram for the following student pulse rates (beats/minute taken at the beginning of a lecture: beginning-of-lecture pulse rates:

3 page 3 TI81 TI8 TI85 1. Access the stat data editor STAT STAT STAT MATRX 1 1 F 1. Enter data Enter other data points ã ã ã ã Access window to set RANGE WINDOW WINDOW GRAPH class boundaries and F class width 4. Set B738 to 5.5 so no data point falls on class boundary (min pulse œ 53 Set B7+B to 110 so entire histogram fits on screen Set class length to Set C738 to 5 to provide some room below the histogram Allow for maximun class frequency of 1 5. Draw histogram STAT MATRX Y œ Y œ F3 F1 cursor on 1:Hist cursor to on cursor to on CLEAR GRAPH GRAPH 6. Determine frequencies TRACE TRACE use cursor to use cursor to use cursor to use cursor to read approx read freq's and read freq's and read approx. frequencies class boundaries class boundaries frequencies

4 page 4 # Finding B, =ß=ßUßUßand the median " 3 The TI calculators will calculate most of the statistical quantities introduced in this course. We will demonstrate how this is done for 1-variable data by using the pulse data listed in the histogram section. Note that these calculators do not determine U" and U$ as was done in the text or coursepack (recall our comments about different ways to compute percentiles. You probably haven't done anything wrong if you obtain a quartile value from your calculator that differs slightly from the value obtained using the formula in the coursepack or EXCEL. The TI calculators calculate U" and U$ by first finding the median of the data, then taking the median of the lower half of the data (not including the overall median if it is an actual observation to determine U and the median of the upper half of the data to determine U. " $ It is assumed that the pulse data has been entered into the calculator; in the TI-8 and TI- 83 it is assumed the data is in column of the stat editor. P " TI81 TI8 TI85 1. Calculate STAT STAT F1 basic MATRX statistics F1 (use to (use to view others view others #. Calculate = VARS VARS VARS EXIT EXIT # B 3 3 STAT # B # B F5 F3 # B Sorting If you want to find U" and U$ as shown in the coursepack or text, or arrange the data in increasing order for some other reason, the sorting feature is useful. It is assumed that the pulse data from the histogram section has been entered into the calculator; for the TI-8 and TI-83 calculators, it is assumed the data is in column P ". TI81 TI8 TI85 Sort data STAT STAT F3 and display MATRX the sorted list STAT STAT MATRX 1 1 1

5 page 5 Box Plots The TI8 and calculators will construct box plots. The TI8 uses the maximum and minimum B-values to define the whiskers. The will draw this box plot but will also construct a box plot that defines whiskers using 1.5*(interquartile range, shows adjacent values and flags outliers. In addition, the TI8 and will display box plots for as many as 3 data sets simultan-eously on the screen. We will initially show a single box plot using the pulse data in the histogram section. It is assumed that this data is already entered in column P ". TI8 (outliers 1. Set the B-scale below WINDOW WINDOW WINDOW B738 and above B7+B; provide room under box plot (Ymin 5 (Ymin 5 (Ymin. Draw the box plot Y œ Y œ Y œ plot1 to on plot1 to on plot1 to on cursor to P" 1 cursor to 1 1 ALPHA GRAPH ALPHA 1 1 GRAPH GRAPH 3. Read values of median, TRACE TRACE TRACE U", U$, B738, B7+B use, to use, to use, to and outliers see values see values see values Multiple box plots With the TI8 and you can view as many as three box plots simultaneously on the screen. As an example we will enter 0 end-of-lecture pulse data in P # and simultaneously view the box plots for the 3 beginning-of-lecture pulse rates from above that should already be in P " and the 0 end-of-lecture pulse rates in P #. The beginning- and end-of-lecture pulse rates are matched by student; for example, student 1 had a pulse rate of 78 beats/min. at the beginning of the lecture and 74 beats/min. at the end of the lecture (apparently, 3 students did not survive the lecture. End-of-lecture pulse rates (beats per minute:

6 page 6 The table below assumes the 0 end-of-lecture pulse rates have been entered in column P # of the stat editor and that step in the box plot table above has been completed. TI8 (outliers 1. Set the B-scale below WINDOW WINDOW WINDOW B738 for both data sets and above B7+B for both data sets; provide room under box plot (Ymin 5 (Ymin 5 (Ymin. Draw the second box plot Y œ Y œ Y œ plot to on plot to on plot to on cursor to P cursor to 1 ALPHA GRAPH ALPHA 1 1 GRAPH GRAPH 3. Read values of median, TRACE TRACE TRACE U", U$, B738, B7+B use, to use, to use, to and outliers on both see values; see values; see values; plots use, use, use, to switch to switch to switch between plots between plots between plots Note that the lower box plot for the end-of-lecture pulse rates is shifted to the left relative to the upper plot for the beginning-of-lecture pulse rates since the end-of-lecture pulse rates are lower. A third box plot can be drawn by repeating step for a third data set after it has been entered into a column of the stat editor.

7 page 7 Scatterplots, Linear Regression and Correlation with TI 81, 8, 83 and 85 TI To clear old data: nd MATRX to highlight the DATA menu; press then to clear any old data.. To enter new data: nd MATRX to highlight the DATA menu; press 1 to obtain the data entry screen. You are prompted for Bà " enter its value and press. Proceed in the same fashion to enter CßBßCß " # # etc. Don't forget to press after CÞ 8 3. To obtain slope, intercept and correlation: Enter the data as explained above. Press nd MATRX to highlight CALC menu; press to select LinReg; press to obtain the intercept +, slope,, and correlation <. 4. To graph scatterplot and the least squares prediction line: Obtain slope, intercept and correlation as explained in 3 above. 1. Press Y= CLEAR to clear the Y " œ line.. Press VARS to highlight the linear regression (LR screen; press 4 to insert the equation for the least squares prediction line in the ] " œ line. Press nd MATRX to obtain the draw screen; press to draw the scatterplot and the least squares prediction line. You can then press TRACE and use the cursor keys to move along the prediction line to observe sc-values and the corresponding B-values. If the screen is blank press RANGE to adjust the B-variable and C-variable range shown by the axes in the scatterplot. Suppose you have a complicated equation in ] " œ that you don't want to clear (erase; then you can insert the equation for the least squares prediction line into a different ]œ line (say ] # œ by doing the following. Press nd VARS 1 to turn off all ] œ equations; then press nd VARS 3 to turn on the ] # œ line. Press Y= and scroll down to ] # œ, press CLEAR, then go to step above. 5. To obtain scfor a particular value of the independent variable B. Obtain slope, intercept and correlation as explained in 3 above. Say you want the value of Cs when Bœ 5. On a new line in the home screen press 5 STO X T to set Bequal to 5. Press VARS 4 to display the prediction line equation; press to display the value for sc when B œ 5. TI 8 1. To clear old data: If you are going to enter ( Bß C bivariate data in L" and L #, first clear any old data in those columns. Press STAT to obtain the data entry screen. Place the cursor on the list name L" then press CLEAR. Clear L # in the same manner.. To enter new data: Press STAT to obtain the data entry screen. Enter the B-data in the L" list and the C- data in the L # list by pressing after each observation. (The data can be entered in any list columns; L " and L # are used for purposes of explanation. 3. To obtain slope, intercept and correlation:

8 page 8 Enter the data as explained above. Press STAT 3 to access the STAT SetUp menu. Select L" for the Xlist and L # for the Ylist under the row titled -Var Stats. Press STAT 9 to obtain the intercept +, slope,, and correlation <. 4. To graph scatterplot and the least squares prediction line: Obtain slope, intercept and correlation as explained in 3 above. Put the equation of the least squares prediction line into Y " on the ]œ list by pressing ]œ CLEAR VARS 5 7. Then turn off all statistical plots by pressing nd ]œ 4. Obtain the Plot 1 display and turn it on by pressing nd ]œ 1. Select scatterplot by selecting the first icon in row Type ; select L" as the Xlist and L # as the Ylist. To graph the scatterplot and least squares prediction line press ZOOM To obtain scfor a particular value of the independent variable B. Obtain slope, intercept and correlation as explained in 3 above. Say you want the value of Cs when Bœ 5. On a new line in the home screen press 5 STO X,T, to set Bequal to 5. Press VARS 7 to display the prediction line equation; press to display the value for sc when B œ Obtain residuals Obtain slope, intercept, and correlation as in 3. immediately above. Place the equation of the least squares prediction line in ] " œ as described in the second sentence in 4. above. Now define L$ œ] " ÐP" Ñas follows. Press STAT to obtain the data entry screen; place the cursor on the list name L$ using the cursor keys; press nd VARS to get L $ œ] " at the bottom of the data entry screen; then type ( nd 1 to obtain L $ œ] " ÐP" ÑÞThe entries in L $ are now the predicted values of y that correspond to the B's in L" Þ To put the residuals C Cs in L %, in the data entry screen put the cursor on the list name L% and press nd nd 3 to obtain L% œ L# L $ at the bottom of the data entry screen. The residuals are now in L %; use 1-VarStats to find the sum of the squares of the residuals. TI To clear old data: If you are going to enter ( Bß C bivariate data in L" and L #, first clear any old data in those columns. Press STAT to obtain the data entry screen. Place the cursor on the list name L" then press CLEAR. Clear L # in the same manner.. To enter new data: Press STAT to obtain the data entry screen. Enter the B-data in the L" list and the C- data in the L # list by pressing after each observation. (The data can be entered in any list columns; L " and L # are used for purposes of explanation. 3. To obtain slope, intercept and correlation: Enter the data as explained above. Press STAT 8 to obtain the intercept +, # # slope,, correlation < and the square of the correlation <. (If < and < do not appear, press nd 0 and scroll down to DiagnosticOn ; press to obtain < and < # along with + and, in the output. 4. To graph scatterplot and the least squares prediction line: Obtain slope, intercept and correlation as explained in 3 above. Put the equation of the least squares prediction line into Y " on the ]œ list by pressing ]œ CLEAR VARS 5 1. Then turn off all statistical plots by pressing nd ]œ 4. Obtain the Plot 1 display and turn it on by pressing nd ]œ 1. Select scatterplot by selecting the first icon in row Type ; select L" as the Xlist and L # as the Ylist. To graph the scatterplot and least squares prediction line press ZOOM 9.

9 page 9 5. To obtain scfor a particular value of the independent variable B. Obtain slope, intercept and correlation as explained in 3 above. Say you want the value of Cs when Bœ 5. On a new line in the home screen press 5 STO X,T,,n to set B equal to 5. Press VARS 5 1 to display the prediction line equation; press to display the value for sc when B œ Obtain residuals The residuals are automatically computed and stored in a list called RESID. To put the residuals in list L $, press STAT to obtain the data entry screen. Place the cursor on the list name L $ using the cursor keys. Press nd STAT to put the residuals in the L$ column. You can now look at a scatterplot of the residuals (with the B-variable on the B-axis and the residuals on the C-axis using the STATPLOT key (press nd Y=. TI To clear old data: If you are going to enter ( Bß C bivariate data, first clear any old data. Press STAT F F5.. To enter new data: Press STAT F and you will be prompted for Bà " enter the B" value and press enter; you will be prompted for C" ; enter the C" value and press enter. Continue in this manner until you have entered all your data. Don't forget to press after you type in the C 8 value. 3. To obtain slope, intercept and correlation: Enter the data as explained above. Press STAT F1 F to obtain intercept, slope, and correlation. 4. To graph scatterplot and the least squares prediction line: Obtain slope, intercept and correlation as explained in 3 above. Press GRAPH F and set the range of values for the ( Bß C data. Press STAT F3 F F4 to draw the scatterplot and least squares prediction line. 5. To see B and sy values graphically and find sc for a particular B: Press STAT F3 F5 to clear the draw screen. Press GRAPH F1 to obtain C" œ on the screen. Now press STAT F5 MORE MORE F to put the regression equation (RegEq in the C" œ line. Now press GRAPH F4 to draw the prediction line with an active cursor in the middle of the line. Use the cursor keys to move up and down the line; the ( Bß C values are at the bottom of the screen. Press GRAPH MORE MORE F1 to obtain an Bœ prompt at the bottom of the graph screen. Enter the desired value of B(between B738and B7+B and to obtain the corresponding value of Cs. Factorials, permutations, and combinations The TI graphics calculators have the 8! ( 8 facorial, G 8 or ˆ 8 < < (the number of 8 combinations of 8 things taken < at a time, and T< (the number of permutations of 8 things taken < at a time formulas in memory. We illustrate the use of the calculators by finding 6!, ˆ ' %, and ' T Þ %

10 page 10 TI81 TI8 TI85 1. Enter X F 6. Calculate 6! and MATH MATH MATH F1 clear screen CLEAR CLEAR CLEAR CLEAR 3. Calculate ˆ ' % and clear screen MATH MATH MATH F CLEAR CLEAR CLEAR CLEAR To calculate T % ', in line 4 of step 3 substitute for 3 for the TI81, 8, 83. Random number generation The TI graphics calculators have a random number generator that generates 10-digit random numbers between 0 and 1. Random numbers are useful for generating random samples. You can read as many of the digits of the number generated as you need. For example, to form random two-digit numbers, ignore the decimal and read only the first two digits of each number generated. TI81 TI8 TI85 1. Set a random number seed of 3 (each time STO STO STO STO you use the random ALPHA MATH MATH number generator MATH X select a new integer 1 1 F as seed 1 F4. Generate the first MATH MATH MATH random number X F F4 3. Generate another random number Binomial distributions: computing probabilities The has the capability to compute individual and cumulative probabilities for binomial distributions. For individual probabilities the format is binompdf( numtrials,p [,x], where numtrials is the number of trials for the binomial distribution, p is the success probability for each trial, and x is an integer or a list of integers at which the binomial distribution function is evaluated. The square brackets around the x indicate that it is optional; if you do not specify x, a list of probabilities from 0 to numtrials is returned. The binomial pdf is

11 page 11 where 8 œnumtrials. 8 0ÐBÑ œ Š : B Ð" :Ñ 8 B ß B œ!ß "ß á 8 B For a binomial distribution with 10 trials and a success probability of.5 on each trial, in the tables below we find the probability of 4 successes and the probability of 6, 7, or 8 successes. 1. Find TÐB œ 6,7,or 8 1. Find TÐB œ 4Ñ when B is binomial VARS when B is VAR with 8œ 10, :œ.5 0 binomial with œ 10, :œ ( 6 7 8

12 page 1 To compute cumulative probabilities for binomial distributions with the, we use binomcdf(numtrials, p [, B], which computes the probability of B or fewer successes for a binomial distribution with number of trials equal to numtrials and success probability p.b can be a real number or a list of real numbers. The square brackets around B indicate that it is optional; if you do not specify B, a list of cumulative probabilities is returned. As examples, for a binomial distribution with 8œ 13 and :œ.7, we compute the probability of 5 or fewer successes in the left table and the probability of 8 or fewer successes, 9 or fewer successes, and 10 or fewer successes in the right table. 1. Find TÐB Ÿ 5 1. Find TÐB Ÿ 8, when B is binomial VARS TÐB Ÿ 9, and VARS with 8œ 13, :œ.7 ALPHA TÐB Ÿ 10 when ALPHA MATH B is binomial MATH with 8œ13 and :œþ7.7 (

13 page 13 Normal distributions: computing probabilities and plottingthe distributions For a normal distribution with mean. and standard deviation 5, normalpdf(b[,., 5] computes the value of the normal probability density function at the specified B value. and the probability that a normal random variable assumes a value in an interval of the real line. normalcdf(69a/<,9?ß?::/<,9?[,.5, ] computes the probability that a normal random variable with mean. and standard deviation 5 assumes a value between 69A/<,9? and?::/<,9?. The normal curve with mean. and standard deviation 5 can also be graphed by pasting normalpdf(b [,.5, ] to the ] œ list. The brackets around.5, indicate that they are optional; if they are not specified, the defaults are. œ 0 and 5 œ 1. For a normal distribution with mean. œ 35 and standard deviation 5 œ, the table on the left computes the value of the probability density function at 33 and draws the normal curve. The table on the right calculates the probability that a random variable with this normal distribution assumes a value between 3.5 and Ymax œ.5 in the WINDOW screen.. For plotting the normal 1. For a normal distribution, you can set distribution with VARS WINDOW variables Xmin and. œ 35, 5 œ, 1 Xmax so that the mean. falls compute value of 33 between them, and then select density function 0:ZoomFit from the ZOOM at menu., ( comma 1. Compute the probability that VARS.Draw normal ]œ a normal rv with density curve CLEAR. œ 35, 5 œ 3.5 when. œ 35, is between œ VARS and X,T,, GRAPH Note: 1E99 and 1E99 specify minus 3.Examine values TRACE infinity and infinity, on curve use, respective- ly on the to traverse calculator. If you want to view curve the area to the left of upperbound, for example, specify lowerbound œ "E99. Note: 1. For this example, Xmin œ 8, Xmax œ 4, Ymin œ!, t-distribution confidence intervals for a population mean. The is programmed to compute intervals for the mean. of a population when the variance is estimated from the data. It can be done either by entering raw data or summary data. We use the 3 student beginning-of-lecture pulse rates from the histogram section above to illustrate the former in the left table below. The right table shows the procedure for summary data using the end-of-lecture pulse rates.

14 page 14 In the left table below it is assumed the beginning-of-lecture pulse rates have been entered in column P " of the stat editor. It is not necessary to enter the end-of-lecture pulse rates for the right table since we will just use the summary data B and =. 1. Ask for the STAT 1. Ask for the > STAT t confidence confidence interval procedure 8 interval procedure 8. Ask for a 95% cursor to DATA, press Enter confidence interval to be constructed 1 using data in column P" 1.95 Note: 1. If the data is in a column other than P ", then specify its location in List on the TInterval screen...95 is the default confidence level. The confidence level can be changed to any level desired on the C-Level line.. Move cursor to allow entry of B and = for end-of-lecture pulses 3. Enter as the B value Enter as the = value 5. Enter 0 as the 0 sample size 6. Ask for 90%.90 conf. interval t-distribution hypotheses tests for a population mean. The /84 is programmed to perform hypothesis tests for the mean. of a population when the standard deviation is estimated from the data. It can be done either by entering raw data or summary data. We use the 3 student beginning-of-lecture pulse rates from the histogram section above to illustrate the former in the left table below. The right table shows the procedure for summary data using the end-of-lecture pulse rates. In the left table below it is assumed the beginning-of-lecture pulse rates have been entered in column P " of the stat editor. It is not necessary to enter the end-of-lecture pulse rates for the right table since we will just use the summary data B and =.

15 page Ask for the > STAT hypothesis test procedure. Ask for a cursor to DATA, press Enter hypothesis test to be input.!, the L! value of. constructed using data in # " column P".: form of LE Calculate Note: If the data is in a column other than P ", then specify its location in List on the T-Test screen. 1. Ask for the STAT t hypothesis test procedure. Move cursor to allow entry of B and = for input.!, the L value of end-of-lecture pulses 3. Enter as the B value 79.45!. 4. Enter as the = value Enter 0 as the sample size 0 6. specify form.: form of LE of LE Calculate, Enter Confidence intervals for a population proportion : The /84 is programmed to compute confidence intervals for the unknown value of a population proportion : from the data in a single sample. /84 1. Ask for the : STAT confidence interval procedure A (alpha math 1-PropZInt. Ask for a 95% Enter values for confidence B (number of successes interval to be 8 (number of trials constructed C-Level (level of confidence Calculate

16 page 16 Hypothesis testing for a population proportion : The /84 is programmed to perform hypotheses tests for the unknown value of a population proportion : from the data in a single sample. /84 1. Ask for the : STAT hypothesis testing procedure 5 1-PropZTest. Ask for a Enter values for hypothesis :!, the L! value of : test to be B (number of successes performed 8 (number of trials prop: form of LE Calculate Confidence Intervals for the difference between population proportions Go to the STAT TESTS menu; scroll down to B: -PropZInt x1 and n1 are the number of successes and the sample size, respectively, in sample 1; similarly for x and n Specify the desired confidence level CALCULATE, the press Confidence Intervals for the difference between population means (independent samples Option 1: using raw data from independent samples Input the data into lists, say L1 and L (the data can be input into any lists Go to the STAT TESTS menu; scroll down to 0: -SampTint Select Inpt: Data Specify that you are using data in L1 and L Specify 1 for both frequencies Specify the confidence level Specify Pooled: No CALCULATE, the press Option : using sample statistics Go to the STAT TESTS menu; scroll down to 0: -SampTint Select Inpt: Stats Input both means, standard deviations, and sample sizes Specify the confidence level Specify Pooled: No CALCULATE, the press