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Notes for the TI-83, 83+, 84 Calculator

Module by: Barbara Illowsky, Ph.D., Susan Dean. E-mail the authors

Summary: Notes and tips for using TI-83, TI-83+, and TI-84 calculators for statistics applications.

Quick Tips

Legend

  • generic button represents a button press
  • [ ] represents yellow command or green letter behind a key
  • < > represents items on the screen

To adjust the contrast

Press 2nd button, then hold up button to increase the contrast or down button to decrease the contrast.

To capitalize letters and words

Press alpha button to get one capital letter, or press 2nd button, then alpha button to set all button presses to capital letters. You can return to the top-level button values by pressing alpha button again.

To correct a mistake

If you hit a wrong button, just hit clear button and start again.

To write in scientific notation

Numbers in scientific notation are expressed on the TI-83, 83+, and 84 using E notation, such that...

  • 4.321 E 4 = 4.321×104 4.321 10 4
  • 4.321 E -4 = 4.321×104 4.321 10 4

To transfer programs or equations from one calculator to another:

Both calculators: Insert your respective end of the link cable cable and press 2nd button, then [LINK].

Calculator receiving information:

  1. Step 1. Use the arrows to navigate to and select <RECEIVE>
  2. Step 2. Press enter button

Calculator sending information:

  1. Step 1. Press appropriate number or letter.
  2. Step 2. Use up and down arrows to access the appropriate item.
  3. Step 3. Press enter button to select item to transfer.
  4. Step 4. Press right arrow to navigate to and select <TRANSMIT>.
  5. Step 5. Press enter button

Note:

ERROR 35 LINK generally means that the cables have not been inserted far enough.
Both calculators: Insert your respective end of the link cable cable Both calculators: press 2nd button, then [QUIT] To exit when done.

Manipulating One-Variable Statistics

Note:

These directions are for entering data with the built-in statistical program.
Table 1: Sample Data
We are manipulating 1-variable statistics.
Data Frequency
-2 10
-1 3
0 4
1 5
3 8

To begin:

  1. Step 1. Turn on the calculator.


    on button

  2. Step 2. Access statistics mode.


    stat button

  3. Step 3. Select <4:ClrList> to clear data from lists, if desired.


    four button , enter button

  4. Step 4. Enter list [L1] to be cleared.


    2nd button , [L1] , enter button

  5. Step 5. Display last instruction.


    2ndbutton , [ENTRY]

  6. Step 6. Continue clearing remaining lists in the same fashion, if desired.


    left button , 2nd button , [L2] , enter button

  7. Step 7. Access statistics mode.


    stat button

  8. Step 8. Select <1:Edit . . .>


    enter button

  9. Step 9. Enter data. Data values go into [L1]. (You may need to arrow over to [L1])
    • Type in a data value and enter it. (For negative numbers, use the negate (-) key at the bottom of the keypad)


      negate button , nine button , enter button

    • Continue in the same manner until all data values are entered.
  10. Step 10. In [L2], enter the frequencies for each data value in [L1].
    • Type in a frequency and enter it. (If a data value appears only once, the frequency is "1")


      four button , enter button

    • Continue in the same manner until all data values are entered.
  11. Step 11. Access statistics mode.


    stat button

  12. Step 12. Navigate to <CALC>
  13. Step 13. Access <1:1-var Stats>


    enter button

  14. Step 14. Indicate that the data is in [L1]...


    2nd button , [L1] , comma button

  15. Step 15. ...and indicate that the frequencies are in [L2].


    2nd button , [L2] , enter button

  16. Step 16. The statistics should be displayed. You may arrow down to get remaining statistics. Repeat as necessary.

Drawing Histograms

Note:

We will assume that the data is already entered

We will construct 2 histograms with the built-in STATPLOT application. The first way will use the default ZOOM. The second way will involve customizing a new graph.

  1. Step 1. Access graphing mode.


    2nd button , [STAT PLOT]

  2. Step 2. Select <1:plot 1> To access plotting - first graph.


    enter button

  3. Step 3. Use the arrows navigate go to <ON> to turn on Plot 1.


    <ON> , enter button

  4. Step 4. Use the arrows to go to the histogram picture and select the histogram.
    enter button
  5. Step 5. Use the arrows to navigate to <Xlist>
  6. Step 6. If "L1" is not selected, select it.


    2nd button , [L1] , enter button

  7. Step 7. Use the arrows to navigate to <Freq>.
  8. Step 8. Assign the frequencies to [L2].


    2nd button , [L2] , enter button

  9. Step 9. Go back to access other graphs.


    2nd button , [STAT PLOT]

  10. Step 10. Use the arrows to turn off the remaining plots.
  11. Step 11. Be sure to deselect or clear all equations before graphing.

To deselect equations:

  1. Step 1. Access the list of equations.


    Y= button

  2. Step 2. Select each equal sign (=).


    down button right button enter button

  3. Step 3. Continue, until all equations are deselected.

To clear equations:

  1. Step 1. Access the list of equations.


    Y= button

  2. Step 2. Use the arrow keys to navigate to the right of each equal sign (=) and clear them.


    down button right button clear button

  3. Step 3. Repeat until all equations are deleted.

To draw default histogram:

  1. Step 1. Access the ZOOM menu.


    ZOOM button

  2. Step 2. Select <9:ZoomStat>


    nine button

  3. Step 3. The histogram will show with a window automatically set.

To draw custom histogram:

  1. Step 1. Access window button to set the graph parameters.
  2. Step 2.
    • X min =2.5 X min 2.5
    • X max =3.5 X max 3.5
    • X scl =1 X scl 1 (width of bars)
    • Y min =0 Y min 0
    • Y max =10 Y max 10
    • Y scl =1 Y scl 1 (spacing of tick marks on y-axis)
    • X res =1 X res 1
  3. Step 3. Access graph button to see the histogram.

To draw box plots:

  1. Step 1. Access graphing mode.


    2nd button , [STAT PLOT]

  2. Step 2. Select <1:Plot 1> to access the first graph.


    enter button

  3. Step 3. Use the arrows to select <ON> and turn on Plot 1.


    enter button

  4. Step 4. Use the arrows to select the box plot picture and enable it.


    enter button

  5. Step 5. Use the arrows to navigate to <Xlist>
  6. Step 6. If "L1" is not selected, select it.


    2nd button , [L1] , enter button

  7. Step 7. Use the arrows to navigate to <Freq>.
  8. Step 8. Indicate that the frequencies are in [L2].


    2nd button , [L2] , enter button

  9. Step 9. Go back to access other graphs.


    2nd button , [STAT PLOT]

  10. Step 10. Be sure to deselect or clear all equations before graphing using the method mentioned above.
  11. Step 11. View the box plot.


    graph button , [STAT PLOT]

Linear Regression

Sample Data

The following data is real. The percent of declared ethnic minority students at De Anza College for selected years from 1970 - 1995 was:

Table 2: The independent variable is "Year," while the independent variable is "Student Ethnic Minority Percent."
Year Student Ethnic Minority Percentage
1970 14.13
1973 12.27
1976 14.08
1979 18.16
1982 27.64
1983 28.72
1986 31.86
1989 33.14
1992 45.37
1995 53.1
Figure 1: By hand, verify the scatterplot above.
Student Ethnic Minority Percentage
A scatterplot of the ethnic minority percentages listed in the above chart, plotted from 1960 to 2000.

Note:

The TI-83 has a built-in linear regression feature, which allows the data to be edited.The x-values will be in [L1]; the y-values in [L2].

To enter data and do linear regression:

  1. Step 1. ON Turns calculator on


    on button

  2. Step 2. Before accessing this program, be sure to turn off all plots.
    • Access graphing mode.


      2nd button , [STAT PLOT]

    • Turn off all plots.


      four button , enter button

  3. Step 3. Round to 3 decimal places. To do so:
    • Access the mode menu.


      mode button , [STAT PLOT]

    • Navigate to <Float> and then to the right to <3>.


      down button right button

    • All numbers will be rounded to 3 decimal places until changed.


      enter button

  4. Step 4. Enter statistics mode and clear lists [L1] and [L2], as describe above.


    stat button , four button

  5. Step 5. Enter editing mode to insert values for x and y.


    stat button , enter button

  6. Step 6. Enter each value. Press enter button to continue.

To display the correlation coefficient:

  1. Step 1. Access the catalog.


    2nd button , [CATALOG]

  2. Step 2. Arrow down and select <DiagnosticOn>


    down button... , enter button , enter button

  3. Step 3. r r and r2 r 2 will be displayed during regression calculations.
  4. Step 4. Access linear regression.


    stats button right button

  5. Step 5. Select the form of y=a+bx y a b x


    eight button , enter button

The display will show:

LinReg

  • y=a+bx y a b x
  • a=3176.909 a 3176.909
  • b=1.617 b 1.617
  • r2=0.924 r 2 0.924
  • r=0.961 r 0.961

This means the Line of Best Fit (Least Squares Line) is:

  • y=3176.909+1.617x y 3176.909 1.617 x
  • Percent=3176.909+1.617(year #) Percent 3176.909 1.617 (year #)
The correlation coefficient r=0.961 r 0.961

To see the scatter plot:

  1. Step 1. Access graphing mode.


    2nd button , [STAT PLOT]

  2. Step 2. Select <1:plot 1> To access plotting - first graph.


    enter button

  3. Step 3. Navigate and select <ON> to turn on Plot 1.


    <ON> enter button

  4. Step 4. Navigate to the first picture.
  5. Step 5. Select the scatter plot.


    enter button

  6. Step 6. Navigate to <Xlist>
  7. Step 7. If [L1] is not selected, press 2nd button , [L1] to select it.
  8. Step 8. Confirm that the data values are in [L1].


    <ON> enter button

  9. Step 9. Navigate to <Ylist>
  10. Step 10. Select that the frequencies are in [L2].


    2nd button , [L2] , enterbutton

  11. Step 11. Go back to access other graphs.


    2nd button , [STAT PLOT]

  12. Step 12. Use the arrows to turn off the remaining plots.
  13. Step 13. Access window button to set the graph parameters.
    • X min =1970 X min 1970
    • X max =2000 X max 2000
    • X scl =10 X scl 10 (spacing of tick marks on x-axis)
    • Y min =0.05 Y min 0.05
    • Y max =60 Y max 60
    • Y scl =10 Y scl 10 (spacing of tick marks on y-axis)
    • X res =1 X res 1
  14. Step 14. Be sure to deselect or clear all equations before graphing, using the instructions above.
  15. Step 15. Press graph button to see the scatter plot.

To see the regression graph:

  1. Step 1. Access the equation menu. The regression equation will be put into Y1.


    Y= button

  2. Step 2. Access the vars menu and navigate to <5: Statistics>


    vars button , five button

  3. Step 3. Navigate to <EQ>.
  4. Step 4. <1: RegEQ> contains the regression equation which will be entered in Y1.


    enter button

  5. Step 5. Press graph button. The regression line will be superimposed over scatter plot.

To see the residuals and use them to calculate the critical point for an outlier:

  1. Step 1. Access the list. RESID will be an item on the menu. Navigate to it.


    2nd button, [LIST], <RESID>

  2. Step 2. Confirm twice to view the list of residuals. Use the arrows to select them.


    enter button , enter button

  3. Step 3. The critical point for an outlier is: 1.9VSSEn2 1.9 V SSE n 2 where:
    • n n = number of pairs of data
    • SSE SSE = sum of the squared errors
    • residual2 residual 2
  4. Step 4. Store the residuals in [L3].


    store button , 2nd button , [L3] , enter button

  5. Step 5. Calculate the (residual)2n2 (residual) 2 n 2 . Note that n2=8 n 2 8


    second button , [L3] , x-squared button , divide button , eight button

  6. Step 6. Store this value in [L4].


    store button , 2nd button , [L4] , enter button

  7. Step 7. Calculate the critical value using the equation above.


    one button , decimal button , nine button , multiply button , 2nd button , [V] , 2nd button , [LIST] right button , right button , five button , 2nd button , [L4] , right parenthesis button , right parenthesis button , enter button

  8. Step 8. Verify that the calculator displays: 7.642669563. This is the critical value.
  9. Step 9. Compare the absolute value of each residual value in [L3] to 7.64 . If the absolute value is greater than 7.64, then the (x, y) corresponding point is an outlier. In this case, none of the points is an outlier.

To obtain estimates of y for various x-values:

There are various ways to determine estimates for "y". One way is to substitute values for "x" in the equation. Another way is to use the trace button on the graph of the regression line.

TI-83, 83+, 84 instructions for distributions and tests

Distributions

Access DISTR (for "Distributions").

For technical assistance, visit the Texas Instruments website at http://www.ti.com and enter your calculator model into the "search" box.

Binomial Distribution

  • binompdf(n,p,x) corresponds to P(X = x)
  • binomcdf(n,p,x) corresponds to P(X ≤ x)
  • To see a list of all probabilities for x: 0, 1, . . . , n, leave off the "x" parameter.

Poisson Distribution

  • poissonpdf(λ,x) corresponds to P(X = x)
  • poissoncdf(λ,x) corresponds to P(X ≤ x)

Continuous Distributions (general)

  • uses the value -1EE99 for left bound
  • uses the value 1EE99 for right bound

Normal Distribution

  • normalpdf(x,μ,σ) yields a probability density function value (only useful to plot the normal curve, in which case "x" is the variable)
  • normalcdf(left bound, right bound, μ,σ) corresponds to P(left bound < X < right bound)
  • normalcdf(left bound, right bound) corresponds to P(left bound < Z < right bound) - standard normal
  • invNorm(p,μ,σ) yields the critical value, k: P(X < k) = p
  • invNorm(p) yields the critical value, k: P(Z < k) = p for the standard normal

Student-t Distribution

  • tpdf(x,df) yields the probability density function value (only useful to plot the student-t curve, in which case "x" is the variable)
  • tcdf(left bound, right bound, df) corresponds to P(left bound < t < right bound)

Chi-square Distribution

  • Χ2pdf(x,df) yields the probability density function value (only useful to plot the chi2 curve, in which case "x" is the variable)
  • Χ2cdf(left bound, right bound, df) corresponds to P(left bound < Χ2 < right bound)

F Distribution

  • Fpdf(x,dfnum,dfdenom) yields the probability density function value (only useful to plot the F curve, in which case "x" is the variable)
  • Fcdf(left bound,right bound,dfnum,dfdenom) corresponds to P(left bound < F < right bound)

Tests and Confidence Intervals

Access STAT and TESTS.

For the Confidence Intervals and Hypothesis Tests, you may enter the data into the appropriate lists and press DATA to have the calculator find the sample means and standard deviations. Or, you may enter the sample means and sample standard deviations directly by pressing STAT once in the appropriate tests.

Confidence Intervals

  • ZInterval is the confidence interval for mean when σ is known
  • TInterval is the confidence interval for mean when σ is unknown; s estimates σ.
  • 1-PropZInt is the confidence interval for proportion

Note:

The confidence levels should be given as percents (ex. enter "95" or ".95" for a 95% confidence level).

Hypothesis Tests

  • Z-Test is the hypothesis test for single mean when σ is known
  • T-Test is the hypothesis test for single mean when σ is unknown; s estimates σ.
  • 2-SampZTest is the hypothesis test for 2 independent means when both σ's are known
  • 2-SampTTest is the hypothesis test for 2 independent means when both σ's are unknown
  • 1-PropZTest is the hypothesis test for single proportion.
  • 2-PropZTest is the hypothesis test for 2 proportions.
  • Χ2-Test is the hypothesis test for independence.
  • Χ2GOF-Test is the hypothesis test for goodness-of-fit (TI-84+ only).
  • LinRegTTEST is the hypothesis test for Linear Regression (TI-84+ only).

Note:

Input the null hypothesis value in the row below "Inpt." For a test of a single mean, "μ∅" represents the null hypothesis. For a test of a single proportion, "p∅" represents the null hypothesis. Enter the alternate hypothesis on the bottom row.

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