Hawkes Learning | Statistics Resources | Technology

Adding Info to Lists

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

Press STAT, select EDIT, Edit, and press ENTER.
Input the data into the lists. See Adding Info to Lists for further help on entering your data.
Press STAT and select TESTS, then choose option ANOVA. Press ENTER.
4. Enter ANOVA (L1, L2, L3). Note that lists can be entered by pressing 2nd followed by the number of the list. For example, 2nd and 1 gives L1.
Press ENTER to display the results.

Binomial Distribution

Binomial Probability (pdf)

Choose DIST (2^nd,VARS).
Scroll down to option binompdf (. Press ENTER.
Input the number of trials, the probability of success, and the number of successes. Hightlight PASTE and then press ENTER.
Press ENTER and then press ENTER to display the probability.

Binomial Probability Distribution

Choose DIST (2^nd,VARS).
Select the option binompdf (. Press ENTER
Input the number of trials and the probability of success. Highlight PASTE and then press ENTER.
To store the probabilities in L2, press STO→ and then (2nd,2).
Press ENTER.
Press STAT.
Choose EDIT and then 1: Edit.Press ENTER.
Input the values 0 to n in L1 to complete the binomial distribution table.

Binomial Probability (cdf)

Press DIST (2^nd,VARS).
Scroll down to option binomcdf (. Press ENTER.
Input the number of trials, the probability of success, and the number of successes. Highlight PASTE and then press ENTER.
Press ENTER to display the cumulative probability.

Chi-Square Distribution

Left Tailed Probability (cdf)

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

Select DISTR by pressing 2^nd and thenVARS.
Select χ²cdf ( from the menu.
Enter (0, χ², degrees of freedom).
Press ENTER.

Right Tailed Probability (cdf)

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

Select DISTR by pressing 2^nd and thenVARS.
Select χ²cdf ( from the menu.
Enter (χ², upper bound, degrees of freedom).
Press ENTER.

Test for Association

Select MATRIX by pressing 2^nd and thenx^-1.
Select EDIT, and [A]. Press ENTER.
Enter the matrix dimensions: number of rows by number of columns. Input the actual data into the matrix with the observed data in the first column [A] of the matrix and the expected values in the second column [B].
Press STAT, select TESTS, and scroll down to χ²-Test. Press ENTER.
Choose Calculate and press ENTER.

Test for Goodness of Fit

Press STAT and select EDIT and Edit….
Input the observed data in L1 and the expected values in L2.
Press STAT, select TESTS, and χ²GOF-Test. Press ENTER.
Enter L₁ for Observed (2^nd, 1), and L₂ for Expected (2^nd, 2).
Enter the appropriate degrees of freedom (df).
Choose Calculate and press ENTER.

Confidence Intervals

Proportion

Press STAT.
Select TESTS from the top menu.
Choose option 1-PropZInt.
Press ENTER.
Input the corresponding values for the variables.
Choose Calculate and press ENTER.
Observe the confidence interval displayed on the screen.

`t-`Interval

Using Summary Statistics

Press STAT.
Select TESTS from the top menu.
Choose option TInterval.
Press ENTER.
Choose Stats and press ENTER.
Input the corresponding values for the variables.
Choose Calculate and press ENTER.
Observe the confidence interval displayed on the screen.

Using Data

Press STAT and navigate to the EDIT menu.
Choose Edit and press ENTER.
Input the data in the column labeled L1, pressing ENTER after each value.
Press QUIT by pressing 2nd and then MODE.
Press STAT and navigate to the TESTS menu.
Choose option TInterval and press ENTER.
Choose Data as the input and press ENTER.
Input the confidence level.
Choose Calculate and press ENTER.
Observe the confidence interval displayed on the screen.

`z-`Interval

Using Summary Statistics

Press STAT.
Select TESTS from the top menu.
Choose option ZInterval.
Press ENTER.
Choose Stats and press ENTER.
Input the corresponding values for the variables.
Choose Calculate and press ENTER.
Observe the confidence interval displayed on the screen.

Using Data

Press STAT and navigate to the EDIT menu
Choose Edit and press ENTER
Input the data in the column labeled L1, pressing ENTER after each value
Choose QUIT by pressing 2nd and then MODE.
Press STAT and navigate to the TESTS menu
Choose option ZInterval and press ENTER.
Choose Data as the input and press ENTER.
Input the confidence interval.
Choose Calculate and press ENTER.
Observe the confidence interval displayed on the screen.

Two Sample z-Interval

Using Summary Statistics

Press STAT.
Select TESTS.
Choose option 2-SampZInt.
Press ENTER.
Choose Stats.
Input the corresponding values for the variables.
Choose Calculate and press ENTER.
Observe the confidence interval displayed on the screen.

Using Data

Press STAT and navigate to the EDIT menu.
Choose Edit and press ENTER.
Input the data for Sample 1 in the column labeled L1, pressing ENTER after each value.
Input the data for Sample 2 in the column labeled L2, pressing ENTER after each value.
Choose QUIT by pressing 2nd and then MODE.
Press STAT and navigate to the TESTS menu.
Choose option 2-SampZInt.
Press ENTER.
Choose Data as the input and press ENTER.
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.
Choose Calculate and press ENTER.

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

Using Summary Statistics

See t-interval, Using Summary Statistics

Using Data

Press STAT and navigate to the EDIT menu.
Choose Edit. Press ENTER.
Input the data for Sample 1 (before data) in the column labeled L1, pressing ENTER after each value.
Input the data for Sample 2 (before data) in the column labeled L2, pressing ENTER after each value.
Highlight L3 and enter the formula L2 (2nd, 2) − L1 (2nd, 1) and then ENTER.
Press STAT and navigate to the TESTS menu.
Choose option TInterval. Press ENTER.
Choose Data as the input and press ENTER.
Input the corresponding values.
1. Enter L3 for List by pressing (2nd, 3).
2. The frequency of the data (Freq) is the default value with is 1.
3. Enter a confidence level.
Choose Calculate and press ENTER.

Two Sample Proportions z-Interval

Press STAT.
Select TESTS from the top menu.
Choose option 2-PropZInt.
Press ENTER.
Input the corresponding values for the variables.
Choose Calculate and press ENTER.
Observe the confidence interval displayed on the screen.

Counting

Combination

Enter the number of objects.
Press MATH.
Select PROB.
Choose nCr.
Press ENTER.
Enter the number of objects taken at a time.
Press ENTER.
Divide 1 by the resulting number of combinations to find the probability of any single combination occurring.

Factorial

Enter the value for which you are calculating the factorial.
Press MATH.
Select PROB.
Choose ! and press ENTER.
Press ENTER.

Permutation

TI-84

Enter the number of objects.
Press MATH.
Select PROB.
Choose nPr.
Press ENTER.
Enter the number of objects you are taking at a time.
Press ENTER.

Descriptive Statistics

One Variable

Press STAT and navigate to the EDIT menu.
Choose Edit and press ENTER.
Input the data in the column labeled L1, pressing ENTER after each value.
Choose QUIT by pressing 2nd and then MODE.
Press STAT and navigate to the CALC menu.
Choose 1-Var Stats and press ENTER.
Press L1 (2nd,1) and press ENTER
Choose Calculate and press ENTER.
The values on the screen will be listed, in order, as follows.

Two Variable

Grouped Data

Press STAT and navigate to the EDIT menu.
Choose Edit and press ENTER.
Input the midpoints of the intervals in the column labeled L1, pressing ENTER after each value.
Input the frequency values in the column labeled L2.
Choose QUIT by pressing 2nd and then MODE.
Press STAT and navigate to the CALC menu.
Choose 1-Var Stats and press ENTER.
Enter L1 (2nd,1) for List and L2 (2nd,2) for FreqList.
Press ENTER.

Variance of a Discrete Random Variable

Press STAT and navigate to the EDIT menu
Choose 1:Edit and press ENTER
Input the x-values in the column labeled L1, pressing ENTER after each value
Input the probabilities in the column labeled L2
Press QUIT (2nd,MODE)
Press STAT and navigate to the CALC menu
Choose 1:1-Var Stats and press ENTER
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.
Press ENTER
Note the standard deviation is returned in the output after the label σx and the variance can be found by squaring this value.

TI-Calculator Variance of a Discrete Random Variable step 10b

Weighted Mean

Press STAT and navigate to the EDIT menu
Choose 1:Edit and press ENTER
Input the frequency values in the column labeled L1, pressing ENTER after each value
Input the weight values in the column labeled L2
Press QUIT (2nd,MODE)
Press STAT and navigate to the CALC menu
Choose 1:1-Var Stats and press ENTER
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.
Press ENTER

`F`-Distribution

`F`-Probability (cdf)

Choose DISTR by pressing 2^nd and then VARS.
Select option Fcdf.
Press ENTER.
Input the lower F value, the upper F value, the numerator degrees of freedom, and the denominator degrees of freedom
Choose Paste and press ENTER. Press ENTER.

Note: If you are finding a probability from negative infinity or to positive infinity, you can enter a large value such as 10E6 using EE (2^nd and then a comma).

Graphs

Histogram

Press STAT and navigate to the EDIT menu. Choose :Edit.
Input the data into a list, pressing ENTER after each value. See Adding Info to Lists for further help on entering your data.
Choose STAT PLOT by pressing 2nd and then Y=. Press ENTER.
Hightlight a plot and then press ENTER.
Select On and the histogram icon, which is the third option in the second row. For Xlist, enter the name of the list where the data is stored.
Select GRAPH to display the histogram. You can resize the graph by pressing WINDOW to adjust the horizontal and vertical scales or by pressing ZOOM and then choose :ZoomStat.

Line Graph

Press STAT and navigate to the EDIT menu. Choose :Edit.
Input the data into a list, pressing ENTER after each value. See Adding Info to Lists for further help on entering your data.
Choose STAT PLOT by pressing 2nd and then Y=. Press ENTER.
Hightlight a plot and then press ENTER.
Select On and the line graph icon, which is the second option in the second row. For Xlist, enter the name of the list where the data to be graphed along the horizontal axis is stored. For Ylist, enter the name of the list where the data to be graphed along the vertical axis is stored.
Select GRAPH to display the histogram. You can resize the graph by pressing ZOOM and then choose :ZoomStat or by pressing WINDOW to adjust the horizontal and vertical scales manually.

Hypothesis Testing

One Proportion `z`-Test

Press STAT.
Select TESTS from the top menu.
Choose 1-PropZTest.
Press ENTER.
Input the values for the test.
Choose Calculate and press ENTER to observe the results of the test.

z-Test

Using Summary Statistics

Press STAT.
Select TESTS from the top menu.
Choose option Z-Test.
Press ENTER.
Choose STATS and press ENTER.
Input the values for the test.
Choose Calculate and then press ENTER to observe the results of the test.

Using Data

Press STAT. Select EDIT and then 1:Edit. Press ENTER.
Input the data into the list. See Adding Info to Lists for further help on entering your data.
Choose QUIT by pressing 2nd and then MODE.
Press STAT. Select TESTS from the top menu.
Choose option Z-Test and press ENTER.
Choose DATA as the input and press ENTER.
Input the corresponding values and the list name where the data is stored.
Choose Calculate and then press ENTER to observe the results of the test.

t-Test

Using Summary Statistics

Press STAT.
Select TESTS from the top menu.
Choose option T-Test.
Press ENTER.
Choose STATS and press ENTER.
Input the values for the test.
Choose Calculate and then press ENTER to observe the results of the test.

Using Data

Press STAT. Select EDIT and then 1:Edit. Press ENTER.
Input the data into the list. See Adding Info to Lists for further help on entering your data.
Choose QUIT by pressing 2nd and then MODE.
Press STAT. Select TESTS from the top menu.
Choose option T-Test and press ENTER.
Choose DATA as the input and press ENTER.
Input the corresponding values and the list name where the data is stored.
Choose Calculate and then press ENTER to observe the results of the test.

Two Proportion z-Test

Press STAT.
Select TESTS from the top menu.
Choose option 2-PropZTest.
Press ENTER.
Input the values for the test.
Choose Calculate and press ENTER to observe the results of the test.

Two Sample `t`-Test (Independent Samples)

Using Summary Statistics

Press STAT.
Select TESTS from the top menu.
Choose option 2-SampTTest.
Press ENTER.
Choose STATS and press ENTER.
6. Input the values for the test. For Pooled: choose “Yes” when assuming that the population variances are equal and choose “No” when assuming that the population variances are not equal.
Choose Calculate and then press ENTER to observe the results of the test. Note: Many calculators use an alternate formula for the number of degrees of freedom so solutions may vary.

Using Data

Press STAT. Select EDIT and then 1:Edit. Press ENTER.
Input the data for Sample 1 into the L1, pressing ENTER after each value. See Adding Info to Lists for further help on entering your data.
Input the data for Sample 2 into the L2, pressing ENTER after each value.
Choose QUIT by pressing 2nd and then MODE.
Press STAT. Select TESTS from the top menu.
Choose option 2-SampTTest and press ENTER.
Choose DATA as the input and press ENTER.
8. Input the corresponding values and the list names where the data is stored. For Pooled: choose “Yes” when assuming that population variances are equal and choose “No” when assuming that the population variances are not equal.
Choose Calculate and then press ENTER to observe the results of the test. Note: 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)

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Using Summary Statistics

See t-Test, using Summary Statistics.

Using Data

Press STAT. Select EDIT and then 1:Edit. Press ENTER.
Input the data for Sample 1 into L1, pressing ENTER after each value. See Adding Info to Lists for further help on entering your data.
Input the data for Sample 2 into L2, pressing ENTER after each value.
Highlight L3 and enter the formula L2 (2nd, 2) − L1 (2nd, 1) and then ENTER.
Choose QUIT by pressing 2nd and then MODE.
Press STAT. Select TESTS from the top menu.
Choose option T-Test and press ENTER.
Choose DATA as the input and press ENTER.
Input the corresponding values and enter L3, the list where the differences are stored.
Choose Calculate and press ENTER to observe the results of the test.

Two Sample `z`-Test

Using Summary Statistics

Press STAT.
Select TESTS from the top menu.
Choose option 2-SampZTest.
Press ENTER.
Choose STATS and press ENTER.
Input the values for the test.
Choose Calculate and then press ENTER to observe the results of the test.

Using Data

Press STAT. Select EDIT and then 1:Edit. Press ENTER.
Input the data for Sample 1 into the L1, pressing ENTER after each value. See Adding Info to Lists for further help on entering your data.
Input the data for Sample 2 into the L2, pressing ENTER after each value.
Choose QUIT by pressing 2nd and then MODE.
Press STAT. Select TESTS from the top menu.
Choose option 2-SampZTest and press ENTER.
Choose DATA as the input and press ENTER.
Input the corresponding values and the list name where the data is stored.
Choose Calculate and then press ENTER to observe the results of the test.

Two Sample `F`-Test

Using Summary Statistics

Press STAT.
Select TESTS from the top menu.
Choose option 2-SampFTest.
Press ENTER.
Choose STATS and press ENTER.
Input the corresponding values.
Choose Calculate and press ENTER to observe the results of the test.

Using Data

Press STAT. Select EDIT and then 1:Edit. Press ENTER.
Input the data for Sample 1 into L1, pressing ENTER after each value. See Adding Info to Lists for further help on entering your data.
Input the data for Sample 2 into L2, pressing ENTER after each value.
Choose QUIT by pressing 2nd and then MODE.
Press STAT. Select TESTS from the top menu.
Choose option 2-SampFTest and press ENTER.
Choose DATA as the input and press ENTER.
Input the corresponding values and the list names where the data is stored.
Choose Calculate and press ENTER to observe the results of the test.

Normal Distribution

Inverse Normal

Choose DISTR by pressing 2^nd and then VARS.
Select option :invNorm.
Press ENTER.
Input the area to the left of z. (If given the area to the right of z, subtract that value from 1.) If using a non-standard normal, then also input the mean and standard deviation
Highlight PASTE and the press ENTER.
Press ENTER to view the result.

Normal Probability (cdf)

Choose DISTR by pressing 2^nd and then VARS.
Select option :normalcdf.
Press ENTER.
Input the lower x or z value, the upper x or z value. Note: If your lower bound is negative infinity or your upper bound is positive infinity, use a very large negative or positive number such as -1E99 or 1E99. E is entered with (2nd, ,).
If using x values, then also input the mean of the distribution (if not entered assumed to be 0) and the standard deviation of the distribution (if not entered assumed to be 1).
Highlight PASTE and then press ENTER.
Press ENTER to display the result.

Normal Probability Graph

Note: To properly view the graph you may need to adjust the WINDOW. Recommended bounds for Xmin and Xmax are ±3σ with Xscl = σ. Let Ymin = -0.1, and Ymax = 1 with Yscl = 0.1.

Choose DISTR by pressing 2^nd and then VARS.
Select DRAW.
Choose option ShadeNorm (.
Press ENTER.
Input the lower x or z value, the upper x or z value. Note: If your lower bound is negative infinity or your upper bound is positive infinity, use a very large negative or positive number such as -1E99 or 1E99. E is entered with (2nd, ,).
If using x values, then also input the mean of the distribution (if not entered assumed to be 0) and the standard deviation of the distribution (if not entered assumed to be 1).
Hightlight DRAW and press ENTER.

Poisson Distribution

Poisson Probability (cdf)

Choose DIST (2^nd,VARS).
Scroll down to option poissoncdf (. Press ENTER.
Input a value for the mean and the number of successes. Highlight PASTE and press ENTER.
Press ENTER to display the cumulative probability.

Poisson Probability (pdf)

Choose DIST (2^nd,VARS).
Scroll down to option poissonpdf (. Press ENTER.
Input a value for the mean and the number of successes. Highlight PASTE and press ENTER.
Press ENTER to display the probability.

Poisson Probability Distribution

Input the values 0 to n in L1.
Choose DIST (2^nd,VARS).
Select poissonpdf (. Press ENTER.
Input the value of the mean. Enter L1 as the probability of success. Highlight PASTE and then press ENTER.
Then store the probabilities in L2, press STO→ and then (2^nd,2).
Press ENTER.
To view the distribution table, press STAT. Select EDIT then 1:Edit. Press ENTER.

Regression

Correlation Coefficient and Coefficient of Determination

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 r².

Select CATALOG by pressing 2nd and then 0.
Scroll down to the option that reads DiagnosticOn.
Press ENTER until the screen says "Done".
Follow the instructions for Simple Linear Regression.

Simple Linear Regression

Finding the Regression Line

Press STAT and navigate to the EDIT menu.
Choose :Edit and press ENTER.
Enter the x-values into L1, and the y-values into L2.
Press QUIT (2nd,MODE).
Press STAT and navigate to the CALC menu.
Choose LinReg(a+bX) and press ENTER.
Choose L1 (2nd,1) for Xlist, L2 (2nd,2) for Ylist. To store the regression equation for graphing, in the Store RegEQ field press VARS and then navigate to Y-Vars and press ENTER. Choose a y-variable from the list and press ENTER.
Choose Calculate ENTER.

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

Calculating the P-value

After finding and storing the regression line, press STAT and navigate to the TESTS menu.
Choose LinRegTTest and press ENTER.
Verify the Xlist, Ylist, and Freq.
Verify ≠0 is selected for β & p.
Put active cursor following RegEQ.
Press VARS.
Choose Y-VARS.
Choose Function.
Press ENTER.
Choose Y1.
Press ENTER.
Move active cursor to Calculate.
Press ENTER.

Standard Error of Estimate

Press STAT.
Choose Edit.
Enter the x-values into L1 and the y-values into L2.
Press STAT.
Choose TESTS.
Choose option LinRegTTest.
Enter L1 for the Xlist and L2 for the Ylist. The value entered for the option Freq should be 1.
Choose ≠0 for the alternative hypothesis to test the significance of the linear relationship.
Enter the regression equation into RegEQ if you have already calculated it. If not, you may leave this blank.
Choose Calculate.
Press Enter.

The standard error of estimate is s.

Sampling

Random Samples

Press MATH, then select PROB and option randInt. Press ENTER, and then input the minimum number (lower), maximum number (upper), and quantity of random numbers desired.
Choose Paste and press ENTER. Press ENTER again. The random numbers are listed on the screen.

`t`-Distribution

Inverse `t`

Choose DIST by pressing 2^nd and then VARS.
Select option invT (.
Press ENTER.
Input the area of the left tail and the degrees of freedom. Select Paste and press ENTER.
Press ENTER again.

`t`-Probability (cdf)

Choose DISTR by pressing 2^nd and then VARS.
Scroll down to option tcdf.
Press ENTER.
Input the lower t value, the upper t value, and the degrees of freedom (df).

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, ,).
Choose Paste and press ENTER. Press ENTER again.

Calculator

Adding Info to Lists

ANOVA

One-Way

Binomial Distribution

Binomial Probability (pdf)

Binomial Probability Distribution

Binomial Probability (cdf)

Chi-Square Distribution

Left Tailed Probability (cdf)

Right Tailed Probability (cdf)

Test for Association

Test for Goodness of Fit

Confidence Intervals

Proportion

t-Interval

Using Summary Statistics

Using Data

z-Interval

Using Summary Statistics

Using Data

Two Sample z-Interval

Using Summary Statistics

Using Data

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

Using Summary Statistics

Using Data

Two Sample Proportions z-Interval

Counting

Combination

Factorial

Permutation

TI-84

Descriptive Statistics

One Variable

Two Variable

Grouped Data

Variance of a Discrete Random Variable

Weighted Mean

F-Distribution

F-Probability (cdf)

Graphs

Histogram

Line Graph

Hypothesis Testing

One Proportion z-Test

z-Test

Using Summary Statistics

Using Data

t-Test

Using Summary Statistics

Using Data

Two Proportion z-Test

Two Sample t-Test (Independent Samples)

Using Summary Statistics

Using Data

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

Using Summary Statistics

Using Data

Two Sample z-Test

Using Summary Statistics

Using Data

Two Sample F-Test

Using Summary Statistics

Using Data

Normal Distribution

Inverse Normal

Normal Probability (cdf)

Normal Probability Graph

Poisson Distribution

Poisson Probability (cdf)

Poisson Probability (pdf)

Poisson Probability Distribution

Regression

Correlation Coefficient and Coefficient of Determination

Simple Linear Regression

Finding the Regression Line

Calculating the P-value

Standard Error of Estimate

Sampling

`t-`Interval

`z-`Interval

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

`F`-Distribution

`F`-Probability (cdf)

One Proportion `z`-Test

Two Sample `t`-Test (Independent Samples)

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

Two Sample `z`-Test

Two Sample `F`-Test

`t`-Distribution

Inverse `t`

`t`-Probability (cdf)