## Quick Tips

Legend

- represents a button press
`[ ]`

represents yellow command or green letter behind a key`< >`

represents items on the screen

To adjust the contrastPress , then hold to increase the contrast or to decrease the contrast.

To capitalize letters and wordsPress to get one capital letter, or press , then to set all button presses to capital letters.You can return to the top-level button values by pressing again.

To correct a mistakeIf you hit a wrong button, just hit and start again.

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

- 4.321 E 4 = $\text{4}\text{.321}\times {\text{10}}^{4}$
- 4.321 E –4 = $\text{4}\text{.321}\times {\text{10}}^{\mathrm{\u20134}}$

To transfer programs or equations from one calculator to another:**Both calculators:** Insert your respective end of the link cable cableand press , then `[LINK]`

.

Calculator receiving information:

- Use the arrows to navigate to and select
`<RECEIVE>`

- Press .

Calculator sending information:

- Press appropriate number or letter.
- Use up and down arrows to access the appropriate item.
- Press to select item to transfer.
- Press right arrow to navigate to and select
`<TRANSMIT>`

. - Press .

### 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 cableBoth calculators: press , then `[QUIT]`

to exit when done.

## Manipulating One-Variable Statistics

### NOTE

These directions are for entering data with the built-in statistical program.

Data | Frequency |
---|---|

–2 | 10 |

–1 | 3 |

0 | 4 |

1 | 5 |

3 | 8 |

Table G1 Sample Data We are manipulating one-variable statistics.

To begin:

Turn on the calculator.

Access statistics mode.

Select

`<4:ClrList>`

to clear data from lists, if desired.

,Enter list

`[L1]`

to be cleared.

,`[L1]`

,Display last instruction.

,`[ENTRY]`

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

, ,`[L2]`

,Access statistics mode.

Select

`<1:Edit . . .>`

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).

, ,- Continue in the same manner until all data values are entered.

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").

,- Continue in the same manner until all data values are entered.

Access statistics mode.

- Navigate to
`<CALC>`

. Access

`<1:1-var Stats>`

.Indicate that the data is in

`[L1]`

...

,`[L1]`

,...and indicate that the frequencies are in

`[L2]`

.

,`[L2]`

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

Access graphing mode.

,`[STAT PLOT]`

Select

`<1:plot 1>`

to access plotting - first graph.Use the arrows navigate go to

`<ON>`

to turn on Plot 1.`<ON>`

,- Use the arrows to go to the histogram picture and select the histogram.
- Use the arrows to navigate to
`<Xlist>`

. If "L1" is not selected, select it.

,`[L1]`

,- Use the arrows to navigate to
`<Freq>`

. Assign the frequencies to

`[L2]`

.

,`[L2]`

,Go back to access other graphs.

,`[STAT PLOT]`

- Use the arrows to turn off the remaining plots.
**Be sure to deselect or clear all equations before graphing.**

To deselect equations:

Access the list of equations.

Select each equal sign (=).

- Continue, until all equations are deselected.

To clear equations:

Access the list of equations.

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

- Repeat until all equations are deleted.

To draw default histogram:

Access the ZOOM menu.

Select

`<9:ZoomStat>`

.- The histogram will show with a window automatically set.

To draw custom histogram:

- Access window mode to set the graph parameters.
- ${X}_{\mathrm{min}}=\mathrm{\u20132.5}$
- ${X}_{\mathrm{max}}=3.5$
- ${X}_{scl}=1$ (width of bars)
- ${Y}_{\mathrm{min}}=0$
- ${Y}_{\mathrm{max}}=10$
- ${Y}_{scl}=1$ (spacing of tick marks on
*y*-axis) - ${X}_{res}=1$

- Access graphing mode to see the histogram.

To draw box plots:

Access graphing mode.

,`[STAT PLOT]`

Select

`<1:Plot 1>`

to access the first graph.Use the arrows to select

`<ON>`

and turn on Plot 1.Use the arrows to select the box plot picture and enable it.

- Use the arrows to navigate to
`<Xlist>`

. If "L1" is not selected, select it.

,`[L1]`

,- Use the arrows to navigate to
`<Freq>`

. Indicate that the frequencies are in

`[L2]`

.

,`[L2]`

,Go back to access other graphs.

,`[STAT PLOT]`

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

,`[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:

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 |

Table G2 The independent variable is "Year," while the independent variable is "Student Ethnic Minority Percent."

Figure G1 Student Ethnic Minority Percentage By hand, verify the scatterplot above.

### 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:

ON Turns calculator on.

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

,`[STAT PLOT]`

Turn off all plots.

,

- Round to three decimal places. To do so:
Access the mode menu.

,`[STAT PLOT]`

Navigate to

`<Float>`

and then to the right to`<3>`

.All numbers will be rounded to three decimal places until changed.

Enter statistics mode and clear lists

`[L1]`

and`[L2]`

, as describe previously.

,Enter editing mode to insert values for

*x*and*y*.

,- Enter each value. Press to continue.

To display the correlation coefficient:

Access the catalog.

,`[CATALOG]`

Arrow down and select

`<DiagnosticOn>`

... , ,- $r$ and${r}^{2}$ will be displayed during regression calculations.
Access linear regression.

Select the form of

*y*=*a*+*bx*.

,

The display will show:

LinReg

*y*=*a*+*bx**a*= –3176.909*b*= 1.617*r*= 2 0.924*r*= 0.961

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

*y*= –3176.909 + 1.617*x*- Percent = –3176.909 + 1.617 (year #)

The correlation coefficient *r* = 0.961

To see the scatter plot:

Access graphing mode.

,`[STAT PLOT]`

Select

`<1:plot 1>`

To access plotting - first graph.Navigate and select

`<ON>`

to turn on Plot 1.`<ON>`

- Navigate to the first picture.
Select the scatter plot.

- Navigate to
`<Xlist>`

. - If
`[L1]`

is not selected, press ,`[L1]`

to select it. Confirm that the data values are in

`[L1]`

.`<ON>`

- Navigate to
`<Ylist>`

. Select that the frequencies are in

`[L2]`

.

,`[L2]`

,Go back to access other graphs.

,`[STAT PLOT]`

- Use the arrows to turn off the remaining plots.
- Access window mode to set the graph parameters.
- ${X}_{\mathrm{min}}=1970$
- ${X}_{\mathrm{max}}=2000$
- ${X}_{scl}=10$ (spacing of tick marks on
*x*-axis) - ${Y}_{\mathrm{min}}=-0.05$
- ${Y}_{\mathrm{max}}=60$
- ${Y}_{scl}=10$ (spacing of tick marks on
*y*-axis) - ${X}_{res}=1$

- Be sure to deselect or clear all equations before graphing, using the instructions above.
- Press the graph button to see the scatter plot.

To see the regression graph:

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

Access the vars menu and navigate to

`<5: Statistics>`

.

,- Navigate to
`<EQ>`

. `<1: RegEQ>`

contains the regression equation which will be entered in Y1.- Press the graphing mode button. The regression line will be superimposed over the scatter plot.

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

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

,`[LIST]`

,`<RESID>`

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

,- The critical point for an outlier is: $1.9V\frac{\mathrm{SSE}}{n-2}$ where:
- $n$ = number of pairs of data
- $\mathrm{SSE}$ = sum of the squared errors
- $\Sigma {\mathrm{residual}}^{2}$

Store the residuals in

`[L3]`

.

, ,`[L3]`

,Calculate the $\frac{{\mathrm{\Sigma residual}}^{2}}{n-2}$. Note that$n-2=8$

,`[L3]`

, , ,Store this value in

`[L4]`

.

, ,`[L4]`

,Calculate the critical value using the equation above.

, , , , ,`[V]`

, ,`[LIST]`

, , , ,`[L4]`

, , ,- Verify that the calculator displays: 7.642669563. This is the critical value.
- 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 on the graph of the regression line.

## TI-83, 83+, 84, 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(`

corresponds to*n*,*p*,*x*)*P*(*X*=*x*)`binomcdf(`

corresponds to*n*,*p*,*x*)*P*(X ≤ x)- To see a list of all probabilities for
*x*: 0, 1, . . . ,*n*, leave off the "

" parameter.*x*

Poisson Distribution

`poissonpdf(λ,`

corresponds to*x*)*P*(*X*=*x*)`poissoncdf(λ,`

corresponds to*x*)*P*(*X*≤*x*)

Continuous Distributions (general)

- $-\infty $ uses the value –1EE99 for left bound
- $\infty $ uses the value 1EE99 for right bound

Normal Distribution

`normalpdf(`

yields a probability density function value (only useful to plot the normal curve, in which case "*x*,*μ*,*σ*)

" is the variable)*x*`normalcdf(left bound, right bound,`

corresponds to*μ*,*σ*)*P*(left bound <*X*< right bound)`normalcdf(left bound, right bound)`

corresponds to*P*(left bound <*Z*< right bound) – standard normal`invNorm(`

yields the critical value,*p*,*μ*,*σ*)*k*:*P*(*X*<*k*) =*p*`invNorm(`

yields the critical value,*p*)*k*:*P*(*Z*<*k*) =*p*for the standard normal

Student's *t*-Distribution

`tpdf(`

yields the probability density function value (only useful to plot the student-*x*,*df*)*t*curve, in which case "

" is the variable)*x*`tcdf(left bound, right bound,`

corresponds to*df*)*P*(left bound <*t*< right bound)

Chi-square Distribution

`Χ`

yields the probability density function value (only useful to plot the chi^{2}pdf(*x*,*df*)^{2}curve, in which case "

" is the variable)*x*`Χ`

corresponds to^{2}cdf(left bound, right bound,*df*)*P*(left bound <*Χ*^{2}< right bound)

F Distribution

`Fpdf(`

yields the probability density function value (only useful to plot the*x*,*dfnum*,*dfdenom*)*F*curve, in which case "

" is the variable)*x*`Fcdf(left bound,right bound,`

corresponds to*dfnum*,*dfdenom*)*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 two independent means when both σ's are known.`2-SampTTest`

is the hypothesis test for two independent means when both σ's are unknown.`1-PropZTest`

is the hypothesis test for single proportion.`2-PropZTest`

is the hypothesis test for two proportions.`Χ`

is the hypothesis test for independence.^{2}-Test`Χ`

is the hypothesis test for goodness-of-fit (TI-84+ only).^{2}GOF-Test`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.