Finding Random Numbers on a TI − 83, 83+, 84+ Calculator

 

Math ¦ ¦ ¦ "PRB" (probability menu)

1:rand generates a random number between 0 and 1

5:randInt ( m , n , k ) generates k random integers between the integers m and n inclusive

(m < n). Put in the appropriate numbers for n, m, and k.

Example: randInt(1,6,2) randomly selects 2 integers between 1 and 6 and returns them in the form of a list between brackets {5 1}. RandInt{1, 6, 2} therefore simulates the act of rolling two dice.

For later in the term:

6:randNorm ( m , s , k ) generates k random values from a Normal probability distribution with mean m and standard deviation s . Use appropriate values for m s k

7:randBin ( n , p , k ) generates k random values from a Binomial probability distribution with n trials and p = probability of success.

TI − 83, 83+, 84+: Entering Data into the statistics list editor

 

STAT "EDIT" Put data into list L1, press ENTER after each data value

2nd QUIT to exit stat list editor after you have entered data, checked it and corrected errors.

 

TI − 83, 83+, 84+: Sorting Data

 

2nd QUIT to exit the statistics list editor

STAT "EDIT" 2 for SORTA sort in ascending order ( 2n d L1 ) The calculator responds DONE

STAT "EDIT" to view the sorted data now stored in L1

2nd QUIT exits the statistics list editor,

 

 

for all TI Graphing Calculators

When you put data into the lists there are two methods to handle repeated values.

Example: Suppose your data is 1, 4, 4, 4, 5, 7, 8, 8.

2 ways to enter data

Enter data in a single list

OR

Use a data list and a frequency list

What the data

looks like:

 

L1

(list each item separately)

1

4

4

4

5

7

8

8

 

 

 

 

L1

(data values)

L2

(frequencies)

1

1

4

3

5

1

7

1

8

2

 

 

 

 

 

 

 

For 1 variable statistics:

TI – 86: One Var L1

TI 83, 84: 1−Var Stats L1

TI – 86: One Var L1, L2

TI 83, 84: 1−Var Stats L1, L2

For statistics plot:

Xlist: L1

Freq: 1

 

Xlist: L1

Freq : L2

 

TI − 83, 83+, 84+: One Variable Statistics

STAT ¦ "CALC" 1 for 1 – Var Stats : one variable summary statistics 2nd L1 ENTER.

If data is in a different list indicate the appropriate listname instead of L1

 

Interpreting The Output For One Variable Statistics

mean

We call this m for a population or a probability distribution; calculator always uses

S x

sum of all data values

 

S x2

squares each data value, then adds them up

 

sx

sample standard deviation

The calculator doesn’t know if your data is a sample or a population, or a probability distribution.

You need to know whether to select the use sx or s x

s x

population standard deviation

n

number of data values

 

MinX

minimum (smallest) data value

 

Q1

value of first (lower) quartile

 

Med

median

 

Q3

value of upper (third) quartile

 

MaxX

minimum (smallest) data value

 

TI − 83, 83+, 84+: Graphing Univariate (One Variable) Data

Histogram using the TI − 83, 83+, 84+:

2nd STATPLOT 1

Highlight "ON" ; press ENTER

To select Type: Highlight histogram icon press ENTER

To set Xlist: 2nd L1 ENTER

To set Freq: 1 ENTER

ZOOM 9 Calculator constructs the histogram, determining its own intervals. Be aware that the calculator may select "strange" intervals because it has no understanding of the context of the data.

To specify your own histogram intervals, adjust the window:

WINDOW

XMin= lower boundary of first interval XMax = upper boundary of last interval

Xscl = interval width

Example: For intervals 15−19, 20−24, 25−29, . . ., 60−64, 65−69:

Xmin = 14.5 Xmax=69.5 Xscl=5

YMin = 0

Estimate YMax to be large enough to display the bar for the interval with the highest frequency. Select an appropriate value of YScl for the tick marks on the y-axis

GRAPH Calculator constructs the histogram with user specified intervals

TRACE then use right and left cursors ° ¦ to move the cursor from bar to bar.

The screen indicates the frequency (height) for the bar that the cursor is positioned on.

Boxplot using the TI − 83, 83+, 84+:

2nd STATPLOT 1

Highlight "ON" ; press ENTER

To select Type: Highlight boxplot icon press ENTER

To set Xlist: 2nd L1 ENTER

To set Freq: 1 ENTER

ZOOM 9 to graph the boxplot

TRACE then right and left cursors ° ¦ move the cursor between the five values defining the boxplot

(min, Q1, median, Q3, max). The screen will indicate the appropriate numerical value.

 

To turn off statistics plots: 2nd STATPLOT 4 (for Plots Off) will turn all statistics plots off.

DIMENSION ERROR message

If you get a dimension error, you probably have one of two types of errors.

One of these methods will usually eliminate a dimension error:

You may be trying to do something with two lists that are supposed to be the same length but for some reason are not. Check that you have the correct information in each list or that you are using the correct lists. Check to be sure that your list is not empty.

You may be trying to graph an equation in your equation editor at the same time as you are trying to graph at STATPLOT. If you want to graph the equation, turn your statplots off. If you want to draw the statplot, go into the Y= equation editor and turn off or delete the functions that are stored in Y1, Y2, . . .

 

PROBABILITY DISTRIBUTIONS SUMMARY on the TI − 83, 83+, 84+, 86, 89

TI-83 and 84, press 2nd DISTR

TI-86 press 2nd MATH MORE; then press F2 or F3 for the STAT menu; press F2:DISTR

TI-89 press APPS; Press 1: FlashApps; highlight Stats/List Editor press ENTER F5: Distr

DISCRETE PROB ABILITY DISTRIBUTIONS: pdf gives P(x = specified value)

cdf gives P(X £ specified value)

function & input

parameters

Description

TI 83,4: binompdf(n,p,r)

TI 86: bipdf(n,p,r)

TI 89: binomial Pdf

n = number of trials

p = probability of success

r = number of success

Binomial probability P(X = r) of exactly r successes in n independent trials, with probability of success p for a single trial. If r is omitted, gives a list of all probabilities from 0 to n

TI 83,4: binomcdf(n,p,r)

TI 86: bicdf(n, p, r)

TI 89: binomial Cdf

n = number of trials

p = probability of success

r = number of success

Binomial cumulative probability P(X £ r) of r or fewer successes in n independent trials, with probability of success p for a single trial.

If r is omitted, gives a list of all cumulative probabilities from 0 to n

TI 83,4: geometpdf(p,n)

TI 86:gepdf(p,n)

TI 89:geometric Pdf

p = probability of success

n = number of trials

Geometric probability P(X = n) that the first success occurs on the nth trial in a series of independent trials, with probability of success p for a single trial.

TI 83,4: geometcdf(p,n)

TI 86:gedf(p,n)

TI 89: geometric Cdf

p = probability of success

n = number of trials

Geometric cumulative probability P(X £ n) that the first success occurs on or before the nth trial in a series of independent trials, with probability of success p for a single trial.

TI 83,4: poissonpdf(m ,r)

TI 86: pspdf(m ,k)

TI 89:Poisson Pdf

m = mean

r = number of occurrences

Poisson probability P(X = r) of exactly r occurrences for a Poisson distribution with mean m

TI 83,4: poissoncdf(m ,r)

TI 86:psdf(m ,r)

TI 89:Poisson cdf

m = mean

r = number of occurrences

Poisson cumulative probability P(X £ r) of r or fewer occurrences for Poisson distribution with

mean m

 

CONTINUOUS PROB ABILITY DISTRIBUTIONS

"cdf" functions find the probability as area under the curve, above x axis within a specified interval of x values. "pdf" functions find the height of the curve above the x axis at a single x value; the "pdf" functions do not find probabilities, but they enable the calculator to draw or graph the curves for the probability distributions.

The inverse functions find the value of a percentile. The only inverse function on the TI-83 and TI-86 is the inverse normal. The TI-84 and 89 have expanded selections of inverse functions.

function & input

parameters

Description

TI 83,4:

normalcdf (c, d, m , s )

TI 86:nmcdf (c, d, m , s )

TI 89:Normal Cdf

c = lower bound

d = upper bound

m = mean

s = standard deviation

P(c < X < d) for a normal distribution with mean m and standard deviation s .

To find P(X>c) use upper bound = 10 ^ 99.

To find P(X < d) use lower bound = (−) 10^ 99, using (−) key to indicate a negative number.

TI 83,4: invNorm(p, m , s )

TI 86:invNm(p, m , s )

TI 89: 2:Inverse }

1: Inverse Normal

p = percentile = area to the left

m = mean

s = standard deviation

Finds the value of x =c for which P(X < c) = p

for a normal distribution with mean m and standard deviation s .

TI 83,4: tcdf(a, b, df)

a = lower bound

b = upper bound

df = degrees of freedom

Probability that a value lies between a and b for a Student's t distribution with the specified degrees of freedom

To find P(X > a), use upper bound = 10 ^ 99.

To find P(X < b), use lower bound = (−) 10 ^ 99, using (−) key to indicate a negative number.

TI 83,4: c 2 cdf(a, b, df)

TI 86:chicdf(a, b, df)

TI 89:Chi-square Cdf

a = lower bound

b = upper bound

df = degrees of freedom

Probability that a value lies between a and b for a c 2 chi-square distribution with the specified degrees of freedom

To find P(X > a), use upper bound = 10 ^ 99.

To find P(X < b), use lower bound = 0.

Binomial, Geometric, Poisson Distributions on the TI − 83, 83+, 84+, 86, 89:

TI-83 and 84, press 2nd DISTR

TI-86 press 2nd MATH MORE and then press F2 or F3 for the STAT menu item F2:DISTR

(menu location of STAT may vary on different calculators)

TI-89 press APPS; pPress 1: FlashApps; highlight Stats/List Editor press ENTER F5: Distr

pdf stands for probability distribution function and gives the probability P(x = r)

cdf stands for cumulative distribution function and gives the probability P(x £ r)

Binomial Distribution

 

TI − 83, 84

TI−86

TI-89

P(x = r)

binompdf(n,p,r)

bipdf(n,p,r)

binomial pdf(n,p,r)

P(x £ r)

binomcdf(n,p,r)

bicdf(n,p,r)

binomial cdf(n,p,r)

P(x < r)

binomcdf(n,p,r−1)

bicdf(n,p,r−1)

binomial cdf(n,p,r−1)

P(x > r)

1− binomcdf(n,p,r)

1− bicdf(n,p,r)

1− binomial cdf(n,p,r)

P(x ³ r)

1− binomcdf(n,p,r−1)

1− bicdf(n,p,r−1)

1− binomial cdf(n,p,r−1)

Geometric Distribution

 

TI − 83, 84

TI−86

TI-89

P(x = n)

geometpdf(p,n)

geopdf(p,n)

geometric pdf(p,n)

P(x £ n)

geometcdf(p,n)

geocdf(p,n)

geometric cdf(p,n)

P(x < n)

geometcdf(p,n−1)

geocdf(p,n−1)

geometric cdf(p,n−1)

P(x > n)

1− geometcdf(p,n)

1− geocdf(p,n)

1− geometric cdf(p,n)

P(x ³ n)

1− geometcdf(p,n−1)

1− geocdf(p,n−1)

1− geometric cdf(p,n−1)

Poisson Distribution

 

TI − 83, 84

TI−86

TI-89

P(x = r)

poissonpdf(mu,r)

pspdf(mu,r)

poisson pdf(mu,r)

P(x £ r)

poissoncdf(mu,r)

pscdf(mu,r)

poisson cdf(mu,r)

P(x < r)

poissoncdf(mu,r−1)

pscdf(mu,r−1)

poisson cdf(mu,r−1)

P(x > r)

1− poissoncdf(mu,r)

1− pscdf(mu,r)

1− poisson cdf(mu,r)

P(x ³ r)

1− poissoncdf(mu,r−1)

1− pscdf(mu,r−1)

1− poisson cdf(mu,r−1)

 

 

TESTS FUNCTIONS SUMMARY on the TI − 83, 83+, 84+, 86, 89

TI-83: STAT } } TESTS

TI-86: 2nd MATH MORE F2 or F3:STAT F1:TESTS

(menu location of STAT may vary on different calculators)

TI-89: APPS 1: FlashApps Highlight Stats/List Editor and press ENTER 2nd F6: Tests

Z-Test

ZTest

Hypothesis test for a single mean, population standard deviation known

 

T-Test

TTest

Hypothesis test for a single mean, population standard deviation unknown, underlying populations approximately normally distributed

2-SampZTest

Zsam2

Hypothesis test of the equality of two population means, independent samples, population standard deviations known

2-SampTTest

Tsam2

Hypothesis test of the equality of two population means, independent samples, population standard deviations unknown, underlying populations approximately normally distributed

1-PropZTest

ZPrp1

Hypothesis test of a single proportion

 

2-PropZTest

ZPrp2

Hypothesis test of the equality of two population proportions

 

ZInterval

ZInt1

Confidence interval for a single mean, population standard deviation known

TInterval

TInt1

Confidence interval for a single mean, population standard deviation unknown, underlying populations approximately normally distributed

2-SampZ Int

ZInt2

Confidence interval for the difference between two means, population standard

deviations known

2-SampT Int

TInt2

Confidence interval for the difference between two means, population standard deviations unknown, underlying populations approximately normally distributed

1-PropZInt

ZInt1

Confidence Interval for a single population proportion

2-PropZInt

ZInt2

Confidence Interval for the difference between two population proportions

c 2 Test

Chitst

Chi2 2-way

Hypothesis test of independence for a contingency table stored in a matrix. Expected values are calculated and placed in a separate matrix

c 2 GOF Test

(TI-84 & 89 Only)

Hypothesis test for Goodness of Fit

Observed and expected data counts must be placed in lists

2-SampFTest

Fsam2

Hypothesis test of the equality of two population standard deviations

 

LinRegTTest

TLinR

Hypothesis test of the signficance of the correlation coefficient in linear regression

 

ANOVA

Hypothesis test of the equality of means of multiple populations using one way analysis of variance for sample data entered into lists

 

Linear Regression and Correlation: Drawing a Scatterplot

on the TI − 83, 83+, 84+ in a window sized to show the data

TI − 83, 83+, 84+: 2nd STATPLOT 1

On Off

Type Highlight the scatterplot icon and press enter

Xlist: list with x variable

Ylist: list with y variable

Mark: select the mark you would like to use for the data points

ZOOM 9:ZoomStat

You can use TRACE and the right and left cursor arrow keys to jump between the data points and show their (x,y) values

To show the linear regression line, type the equation of the line into function Y1 in the Y= function editor.

TI − 83, 83+, 84+: Y= Enter the equation into Y1 as Y1 = a + bX, using the appropriate values for

a and b in the equation. You can enter X using the X,t,q ,n key

 

Setting up your TI – 83 & 84:

2nd catalog (above 0 key) D(above x –1 key) scroll down to Diagnostics On

With the cursor pointing to Diagnostics on press Enter

When Diagnostics On is pasted to your home screen, press Enter again

You should only need to do this once. After you have turned Diagnostics ON it should stay on unless

you turn it off, reset your memory, or your batteries and the backup battery both go dead.

 

Linear Regression Using the TI − 83, 83+, 84+: Linear Regression t test

TI − 83, 83+, 84+: STAT TESTS E:LinRegTTest

Xlist: list with x variable

Ylist: list with y variable

Freq: 1

b & r : ¹ 0 <0 >0

RegEQ: leave blank

Calculate

ENTER

OUTPUT of Linear Regression t test

LinRegTTest

y = a + bx

b ¹ 0 and r ¹ 0

t = test statistic

p = p-value

df = n - 2

a = value of y-intercept

b = value of slope

s = standard error

r2 = value of coefficient of determination

r = value of correlation coefficient

 

The linear regression equation is stored in the graphing equation editor as function Y1 on TI-83, 83+ & 84+. If you select this function to be on when you graph the scatterplot of the data, the graph will also show the least squares linear regression line on the scatterplot of the data

If you have trouble entering the equation name into the test window, you can type the equation into Y1 manually after you perform the test (see scatterplot instructions on previous page)

 

Linear Regression and Correlation:

Identifying Outliers in Bivariate Data graphically using the TI calculators

Perform the linear regression using the Linear Regression T Test Function

Write down the value of the Standard Error s, the slope b and the y-intercept a

Go to the Y= equation editor. Type the linear regression equation into equation Y1: Y1 = a + bX, using the appropriate values for a and b in the equation. You can enter X using the X,t,q ,n key

Enter two new equations: Y2 = a + bX − 2 * s and Y3 = a + bX + 2 * s

using the appropriate values of a, b, and the standard error s in the equations

Draw the graph: press ZOOM 9:ZoomStat

An outlier is any point for which the data value is more than two standard errors away from the linear regression line.

Any points that lie above the top line or below the bottom line are outliers, being more than two standard errors away from the regression line. Any points that lie between the lines are NOT outliers.

Use TRACE and the right and left arrow keys to identify which are the points that are the outliers and to find the x and y values for these data points.

Test of Independence for TI-83, 83+, 84+

  1. Access MATRIX menu to input data to matrix A:
  2. TI83 : MATRIX EDIT ENTER

    TI83+ & 84+ : 2nd MATRIX EDIT ENTER

  3. Enter matrix dimensions:
  4. Type: # rows ENTER # columns ENTER

  5. Enter table values going across rows
  6. Press ENTER after each value. When done, press EXIT.

  7. Run program to do Chi Test
  8. TI83, 83+ & 84+ STAT TESTS C: -TEST

    Make sure Observed says A and Expected says B.

    Press CALC or Calculate

    You will see the test statistic and p-value on the screen.

  9. To see the expected values matrix

TI83, 83+ & 84+ MATRIX 2 ENTER

Warning about Chi Square Test for Independence
When you use your calculator for a chi square test for independence you should ALWAYS use CALC (calculate) and you should not use DRAW. You should draw your graph yourself, using your knowledge of that this test is always a right tailed test.

There is a bug in the calculator program for chi test using DRAW. Sometimes it shades the graph in the wrong direction.

A chi test for independence is always a one tailed test to the right (because you are testing whether the chi square test statistic is a large number, indicating large differences between observed and expected).

If you have the calculator draw, it may shade to the right correctly, or it may incorrectly shade to the left instead. The direction of the shading appears to be related to the direction of the last z, t, or proportion hypothesis test that was done on the calculator. If the last test of a mean or a proportion was two tailed or right tailed, it seems to shade to the right, correctly. If the last test of a mean or a proportion was left tailed, it incorrectly shades left instead of right.