# Calculator

1. To access lists, press STAT, select EDIT, 1: Edit, and ENTER.

2. To clear a list, navigate so that your focus is on the name of the list, such as L2, then press CLEAR, then ENTER.

## ANOVA

### One-Way

1. Press STAT, select EDIT, 1: Edit, and press ENTER.

2. Input the data into the lists. See Adding Info to Lists for further help on entering your data.

3. Press STAT and select TESTS, scroll down to select option ANOVA and press ENTER.

4. Use (2nd, #) and , to enter the appropriate lists separated by commas. Press ).

5. Press ENTER.

## Binomial Distribution

### Binomial Probability (pdf)

1. Choose DIST (2nd,VARS).

2. Scroll down to option binompdf. Press ENTER.

3. Input the number of trials, the probability of success, and the number of successes seperated by commas. Press ), ENTER.

### Binomial Probability Distribution

#### TI-84

1. Choose DIST (2nd,VARS).

2. Select 0:binompdf.

3. Press ENTER.

4. Input the number of trials and the probability of success.

5. Close the parentheses.

6. Then store the list in L2 by pressing STO→L2 (2nd,2).

7. Press ENTER.

8. Press STAT.

9. Choose EDIT.

10. Select Edit.

11. Press ENTER.

12. Input the values 0 to n in L1.

### Binomial Probability (cdf)

1. Choose DIST (2nd,VARS).

2. Scroll down to option binomcdf. Press ENTER.

3. Input the number of trials, the probability of success, and the number of successes separated by commas. Press ), ENTER.

## Chi-Square Distribution

### Left Tailed Probability (cdf)

#### TI-84

Used for finding the p-value corresponding to a χ2 test statistic.

1. Select DISTR (2nd,VARS).

2. Select 7: χ2cdf(

3. Enter (0, χ2, degrees of freedom)

4. Press ENTER.

### Right Tailed Probability (cdf)

#### TI-84

Used for finding the p-value corresponding to a χ2 test statistic.

1. Select DISTR (2nd,VARS).

2. Select 7: χ2cdf(

3. Enter 2, upper bound, degrees of freedom)

4. Press ENTER.

### Test for Association

1. For TI-83, press MATRIX. For TI-83 Plus and TI-84 Plus press MATRIX ( 2nd, x-1).

2. Select EDIT, and 1:A. Press ENTER.

3. Enter the matrix dimensions: number of rows by number of columns. Input the actual data into the matrix.

4. Press STAT, select TESTS, and scroll down to x2-Test. Press ENTER.

5. Choose Calculate and press ENTER.

### Test for Goodness of Fit

#### TI-84 Plus

Other TI-83/84 calculators do not have this test built in.

1. Press STAT and select EDIT and Edit….

2. Input observed data in L1 and expected in L2.

3. Press STAT, select TESTS, and D: χ2GOF-Test. Press ENTER.

4. Enter L1 for Observed, and L2 for Expected.

5. Enter the appropriate degrees of freedom.

6. Choose Calculate and press ENTER.

## Confidence Intervals

### Proportion

##### TI-84
1. Press STAT.

2. Select TESTS.

3. Choose option A:1-PropZInt.

4. Press ENTER.

5. Choose Stats.

6. Input the corresponding values for the variables.

7. Choose Calculate and press ENTER.

8. Observe the confidence interval listed on the screen.

### t-Interval

#### TI-84

##### Using summary statistics
1. Press STAT.

2. Select TESTS.

3. Choose option 8: TInterval.

4. Press ENTER.

5. Choose Stats.

6. Input the corresponding values for the variables.

7. Choose Calculate and press ENTER.

8. Observe the confidence interval listed on the screen.

##### Using data
1. Press STAT and navigate to the EDIT menu

2. Choose 1:Edit and press ENTER

3. Input the data in the column labeled L1, pressing ENTER after each value

4. Press QUIT (2nd,MODE)

5. Press STAT and navigate to the TESTS menu

6. Choose option 8: TInterval.

7. Press ENTER.

8. Choose data.

9. Input the corresponding values.

10. Choose Calculate and press ENTER.

11. Observe the confidence interval listed on the screen.

### z-Interval

#### TI-84

##### Using summary statistics
1. Press STAT.

2. Select TESTS.

3. Choose option 7: ZInterval.

4. Press ENTER.

5. Choose Stats.

6. Input the corresponding values for the variables.

7. Choose Calculate and press ENTER.

8. Observe the confidence interval listed on the screen.

##### Using data
1. Press STAT and navigate to the EDIT menu

2. Choose 1:Edit and press ENTER

3. Input the data in the column labeled L1, pressing ENTER after each value

4. Press QUIT (2nd,MODE)

5. Press STAT and navigate to the TESTS menu

6. Choose option 7: ZInterval.

7. Press ENTER.

8. Choose data.

9. Input the corresponding values.

10. Choose Calculate and press ENTER.

11. Observe the confidence interval listed on the screen.

### Two Sample z-Interval

#### TI-84

##### Using summary statistics
1. Press STAT.

2. Select TESTS.

3. Choose option 9: 2-SampZInt.

4. Press ENTER.

5. Choose Stats.

6. Input the corresponding values for the variables.

7. Choose Calculate and press ENTER.

8. Observe the confidence interval listed on the screen.

##### Using data
1. Press STAT and navigate to the EDIT menu

2. Choose 1:Edit and press ENTER

3. Input the data for sample 1 in the column labeled L1, pressing ENTER after each value

4. Input the data for sample 2 in the column labeled L2, pressing ENTER after each value

5. Press QUIT (2nd,MODE)

6. Press STAT and navigate to the TESTS menu

7. Choose option 9: 2-SampZInt.

8. Press ENTER.

9. Choose data.

10. Input the corresponding values. Use 2nd and the number keys to enter the names of the lists. The frequency for each list should be 1.

11. Choose Calculate and press ENTER.

12. Observe the confidence interval listed on the screen.

### Two Sample t-Interval (Dependent Samples, Paired Difference)

#### TI-84

##### Using data
1. Enter the data in the lists L1 and L2. Let L1 be the "before" levels and L2 be the "after" levels. See Adding Info to Lists for further help on entering your data.

2. Highlight L3 and enter the formula L2 (2nd,2)– L1 (2nd,1) and then ENTER.

3. Press STAT and navigate to the TESTS menu.

4. Choose option TInterval. Press ENTER.

5. Choose the Data option.

6. Input the corresponding values.

1. Enter L3 for List by pressing (2nd, 3).

2. The frequency of the data (Freq) is the default value which is 1.

3. Enter a confidence level.

7. Choose Calculate and press ENTER.

### Two Sample Proportions z-Interval

#### TI-84

1. Press STAT.

2. Select TESTS.

3. Choose option B: 2-PropZInt.

4. Press ENTER.

5. Choose Stats.

6. Input the corresponding values for the variables.

7. Choose Calculate and press ENTER.

8. Observe the confidence interval listed on the screen.

## Counting

### Combination

#### TI-84

1. Enter the number of objects.

2. Press MATH.

3. Select PRB.

4. Choose 3:nCr.

5. Press ENTER.

6. Enter the number of objects taken at a time.

7. Press ENTER.

8. Divide 1 by the resulting number of combinations to find the probability of any single combination occurring.

### Factorial

#### TI-84

1. Enter the value for which you are calculating the factorial.

2. Press MATH.

3. Select PRB.

4. Choose 4:!

5. Press ENTER.

### Permutation

#### TI-84

1. Enter the number of objects.

2. Press MATH.

3. Select PRB.

4. Choose 2:nPr.

5. Press ENTER.

6. Enter the number of objects you are taking at a time.

7. Press ENTER.

## Descriptive Statistics

### One Variable

#### TI-84

1. Press STAT and navigate to the EDIT menu

2. Choose 1:Edit and press ENTER

3. Input the data in the column labeled L1, pressing ENTER after each value

4. Press QUIT (2nd,MODE)

5. Press STAT and navigate to the CALC menu

6. Choose 1:1-Var Stats and press ENTER

7. Press L1 (2nd,1) and press ENTER

8. The values on the screen will be listed, in order, as follows.

### Two Variable

#### TI-84

##### Grouped Data
1. Press STAT and navigate to the EDIT menu

2. Choose 1:Edit and press ENTER

3. Input the midpoints of the intervals in the column labeled L1, pressing ENTER after each value

4. Input the frequency values in the column labeled L2

5. Press QUIT (2nd,MODE)

6. Press STAT and navigate to the CALC menu

7. Choose 1:1-Var Stats and press ENTER

8. Press L1 (2nd,1), then insert a comma and press L2 (2nd,2). On some calculators, 1-Var Stats may bring up a form with labels List and FreqList. Enter L1 (2nd,1) for List and L2 (2nd,2) for FreqList.

9. Press ENTER

##### Variance of a Discrete Random Variable
1. Press STAT and navigate to the EDIT menu

2. Choose 1:Edit and press ENTER

3. Input the x-values in the column labeled L1, pressing ENTER after each value

4. Input the probabilities in the column labeled L2

5. Press QUIT (2nd,MODE)

6. Press STAT and navigate to the CALC menu

7. Choose 1:1-Var Stats and press ENTER

8. Press L1 (2nd,1), then insert a comma and press L2 (2nd,2). On some calculators, 1-Var Stats may bring up a form with labels List and FreqList. Enter L1 (2nd,1) for List and L2 (2nd,2) for FreqList.

9. Press ENTER

10. Note the standard deviation is returned in the output after the label σx and the variance can be found by squaring this value.

##### Weighted Mean
1. Press STAT and navigate to the EDIT menu

2. Choose 1:Edit and press ENTER

3. Input the weight values in the column labeled L1, pressing ENTER after each value

4. Input the frequency values in the column labeled L2

5. Press QUIT (2nd,MODE)

6. Press STAT and navigate to the CALC menu

7. Choose 1:1-Var Stats and press ENTER

8. Press L1 (2nd,1), then insert a comma and press L2 (2nd,2).

On some calculators, 1-Var Stats may bring up a form with labels List and FreqList. Enter L1 (2nd,1) for List and L2 (2nd,2) for FreqList.

9. Press ENTER

## F-Distribution

### F-Probability (cdf)

#### TI-83

1. Choose DISTR (2nd,VARS).

2. Select option 9:Fcdf.

3. Press ENTER.

4. Input the lower F value , the upper F value , the numerator degrees of freedom , the denominator degrees of freedom

Note: If you are finding a probability from negative infinity or to positive infinity, you can enter a large value such as 10E6 (E entered with 2nd ,).

## Graphs

### Histogram

#### TI-84

1. First enter your data into the calculator by pressing STAT and choosing 1:Edit. Type your data into the first list, L1.

2. Your calculator screen should look similar to the following screenshot.

3. Choose STAT PLOT by pressing 2nd,Y=.

4. Press ENTER

5. Select On and the histogram graph, which is the third option. Press ENTER.

6. Select GRAPH to display the histogram. You can resize the graph by pressing ZOOM and then choosing 9:ZoomStat.

### Line Graph

#### TI-84

1. Enter the data by pressing STAT and choosing 1:EDIT. Enter the time variable values in L1 and the measured variable values in L2.

2. Press 2nd and then Y= to display the STAT PLOTS menu. Select the second graph type in the menu and press GRAPH. Use the ZOOM button if necessary and choose option 9:ZoomSTAT to see the line graph below.

## Hypothesis Testing

### One Proportion z-Test

1. Press STAT.

2. Select TESTS. Scroll down to option 1-PropZTest. Press ENTER.

3. Input the coresponding values.

4. Choose Calculate and press ENTER.

### z-Test

1. Press STAT.

2. Select TESTS.

3. Select option 1:Z-Test.

4. Press ENTER.

5. Input the corresponding values.

1. You have the option to input Data or Stats.

1. Data – If you have the raw data and it is a small enough sample where it is reasonable to enter, you will get a more exact answer using this than the summary statistics. See Adding Info to Lists for further help on entering your data.

2. Stats – Use this option if you were provided summary statistics.

6. Choose Calculate and press ENTER.

### t-Test

1. Press STAT.

2. Select TESTS.

3. Select option 2:T-Test.

4. Press ENTER.

5. Input the corresponding values.

1. You have the option to input Data or Stats.

1. Data – If you have the raw data and it is a small enough sample where it is reasonable to enter, you will get a more exact answer using this than the summary statistics. See Adding Info to Lists for further help on entering your data.

2. Stats – Use this option if you were provided summary statistics.

6. Choose Calculate and press ENTER.

### Two Proportion z-Test

1. Press STAT.

2. Select TESTS.

3. Select option 6:2-PropZTest.

4. Press ENTER.

5. Input the coresponding values.

6. Choose Calculate and press ENTER.

### Two Sample t-Test (Independent Samples)

1. Press STAT.

2. Select TESTS.

3. Select option 4:2-SampTTest.

4. Press ENTER.

5. Input the corresponding values.

1. You have the option to input Data or Stats.

1. Data – If you have the raw data and it is a small enough sample where it is reasonable to enter, you will get a more exact answer using this than the summary statistics. See Adding Info to Lists for further help on entering your data.

2. Stats – Use this option if you were provided summary statistics.

6. Select Yes or No for Pooled.

1. Choose Yes if you are assuming the population variances to be equal.

2. Choose No if you are not assuming the population variances to be equal.

7. Choose Calculate and press ENTER.

Note that many calculators use an alternate formula for the number of degrees of freedom, so solutions may vary.

### Two Sample t-Test (Dependent Samples, Paired Difference)

#### Using Data

1. Enter the data in the lists L1 and L2. Let L1 be the "before" levels and L2 be the "after" levels. See Adding Info to Lists for further help on entering your data.

2. Highlight L3 and enter the formula L2 (2nd,2) – L1 (2nd,1) and then ENTER.

3. Press STAT and navigate to the TESTS menu.

4. Choose option T-Test. Press ENTER.

5. Choose the Data option.

6. Input the corresponding values.

1. Enter a value for μ0.

2. Enter L3 for List by pressing (2nd, 3 ).

3. The frequency of the data (Freq) is the default value which is 1.

4. Choose the appropriate alternative hypothesis.

7. Choose Calculate and press ENTER.

### Two Sample z-Test

1. Press STAT.

2. Select TESTS.

3. Select option 3:2-SampZTest.

4. Press ENTER.

5. Input the corresponding values.

1. You have the option to input Data or Stats.

1. Data – If you have the raw data and it is a small enough sample where it is reasonable to enter, you will get a more exact answer using this than the summary statistics. See Adding Info to Lists for further help on entering your data.

2. Stats – Use this option if you were provided summary statistics.

6. Choose Calculate and press ENTER.

### Two Sample F-Test

1. Press STAT.

2. Select TESTS.

3. Scroll down and select option 2-SampFTest.

4. Press ENTER.

5. Input the corresponding values.

1. You have the option to input Data or Stats.

1. Data – If you have the raw data and it is a small enough sample where it is reasonable to enter, you will get a more exact answer using this than the summary statistics. See Adding Info to Lists for further help on entering your data.

2. Stats – Use this option if you were provided summary statistics.

6. Choose Calculate and press ENTER.

## Normal Distribution

### Inverse Normal

#### TI-84

1. Choose DISTR (2nd,VARS).

2. Select option 3:invNorm.

3. Press ENTER.

4. Input the area to the left of z. (If given the area to the right of z, subtract from 1.)

5. (If non-standard normal, input , mean , standard deviation.)

6. Press ENTER.

### Normal Probability (cdf)

#### TI-84

1. Choose DISTR (2nd,VARS).

2. Select option 2:normalcdf.

3. Press ENTER.

4. Input the lower x or z value , the upper x or z value , the mean of the distribution (not required if providing z scores – if not entered assumed to be 0), the standard deviation of the distribution (not required if providing z-scores – if not entered assumed to be 1).

Note: If you are finding a probability from negative infinity or to positive infinity, you can enter a large value such as 10E6 (E entered with 2nd ,).

5. Press ENTER.

### Normal Probability Graph

#### TI-84

1. Choose DISTR (2nd,VARS).

2. Select DRAW.

4. Press ENTER.

5. Input the (lower bound, upper bound, µ, σ).

6. Press ENTER.

Note: To properly view the graph you may need to adjust the WINDOW. In this example Xmin=-30, Xmax=50, Ymin=-0.007, and Ymax=0.025.

## Poisson Distribution

### Poisson Probability (cdf)

1. Choose DIST (2nd,VARS).

2. Scroll down to option poissoncdf. Press ENTER.

3. Input the mean and the number of successes separated by a comma. Press ), ENTER.

### Poisson Probability (pdf)

1. Choose DIST (2nd,VARS).

2. Scroll down to option poissonpdf. Press ENTER.

3. Input the mean and the number of successes separated by a comma. Press ), ENTER.

### Poisson Probability Distribution

#### TI-84

1. Choose DIST (2nd,VARS).

2. Select C:poissonpdf.

3. Press ENTER.

4. Input the mean and the number of successes you want to store the probability for in braces.

5. Close the parentheses.

6. Then store the list in L2 by pressing STO→L2 (2nd,2).

7. Press ENTER.

8. Press STAT.

9. Choose EDIT.

10. Select Edit.

11. Press ENTER.

12. Input the values 0 to n in L1.

## Regression

### Correlation Coefficient and Coefficient of Determination

#### TI-84

For the correlation coefficient (r) and the coefficient of determination (r2) to appear in the output for the linear regression function, the following steps must be taken.

Note: These directions update a setting in your calculator and do not need to be followed every time the linear regression function is run to find r and ${r}^{2}$.

1. Press CATALOG (2nd,0)

2. Scroll down to the option that reads DiagnosticOn

3. Press ENTER until the screen says "Done"

4. Follow the instructions for Simple Linear Regression

### Simple Linear Regression

#### TI-84

##### Finding the Regression Line
1. Press STAT and navigate to the EDIT menu

2. Choose 1:Edit and press ENTER

3. Enter the independent variables into L1, and the dependent variables into L2

4. Press QUIT (2nd,MODE)

5. Press STAT and navigate to the CALC menu

6. Choose 4:LinReg(ax+b) and press ENTER

7. Press L1 (2nd,1), then insert a comma and press L2 (2nd,2)

8. Press ENTER

Note: If Diagnostics are OFF, only the equation and values of a and b will be displayed.

##### Storing the Regression Line
1. After finding the regression line, press Y=.

2. Put active cursor in Y1.

3. Press VARS.

4. Choose 5: Statistics.

5. Choose EQ.

6. Choose 1:RegEQ.

7. Press ENTER.

8. Press STAT.

9. Choose TESTS.

10. Choose E:LinRegTTest.

11. Press ENTER.

##### Calculating the P-value
1. After finding and storing the regression line, press STAT and navigate to the TESTS menu.

2. Choose E:LinRegTTest and press ENTER.

3. Verify the Xlist, Ylist, and Freq.

4. Verify μ0 is selected for β & p.

5. Put active cursor following RegEQ.

6. Press VARS.

7. Choose Y-VARS.

8. Choose 1:Function.

9. Press ENTER.

10. Choose 1:Y1.

11. Press ENTER.

12. Move active cursor to Calculate.

13. Press ENTER.

##### Standard Error of Estimate
1. Press STAT.

2. Choose 1: Edit.

3. Enter the x-values into L1 and the y-values into L2.

4. Press STAT.

5. Choose TESTS.

6. Choose option E: LinRegTTest.

Note: On newer TI-84 Plus calculators, the function LinRegTTest is option F on the TESTS menu.

7. Enter L1 for the Xlist and L2 for the Ylist. The value entered for the option Freq should be 1.

8. Choose μ 0 for the alternative hypothesis to test the significance of the linear relationship.

9. Enter the regression equation into RegEQ if you have already calculated it. If not, you may leave this blank.

10. Choose Calculate.

11. Press Enter.

The standard error of estimate is s, the third-to-last value given.

## Sampling

### Random Samples

#### TI-84

1. Press MATH, then select PRB and option 5:randInt. Press ENTER, and then input the (minimum number, maximum number, quantity of random numbers desired). Press ENTER, and the random numbers are listed on the screen.

## t-Distribution

### Inverse t

#### TI-83

1. Press STAT and navigate to the TESTS menu.

2. Select option 8:TInterval.

3. Press ENTER.

4. Select Stats, set to 0, enter the square root of n (df+1) for Sx, enter n, the confidence level such that (1-confidence level)/2 is the desired right-tailed area and press ENTER. So, in this example we are looking for the t-value such that the area to its left is 0.975.

The upper value of the interval is the desired t-value.

#### TI-84 Plus

1. Choose DISTR (2nd,VARS).

2. Select option 4:tinv.

3. Press ENTER.

4. Input the area of the left tail, the degrees of freedom ) and press ENTER

### t-Probability (cdf)

1. Choose DISTR (2nd,VARS).

2. Scroll down to option tcdf.

3. Press ENTER.

4. Input the lower t value , the upper t value , and the degrees of freedom seperated by commas.

Note: If your lower bound is negative infinity or your upper bound is positive infinity, use a very large negative or positive number as your t value such as -1E99 or 1E99. E is entered with (2nd, ,).

5. Press ), ENTER.