Calculator

Adding Info to Lists

To access lists, press STAT, select Edit from the top menu, choose Edit horizontal ellipsis, and press Enter key.
To input data by column, type a numerical value and press Enter key after each entry. Press the right arrow key to navigate to a new list.
To clear a list, navigate to the name of the list, such as L2, then press Clear, then Enter key.

ANOVA

One-Way

press STAT, select Edit from the top menu, choose Edit horizontal ellipsis, and press Enter key.
Input the data into the lists. See Adding Info to Lists for further help on entering your data.
Press STAT and select TESTS from the top menu, then scroll down to option ANOVA left parenthesis. Press Enter key.
Enter ANOVA left parenthesis L1, L2,L3 right parenthesis. Note that lists can be entered by pressing second followed by the number of the list. For example, second and one gives L1.
Press Enter key to display the results.

Binomial Distribution

Binomial Probability (pdf)

Select DISTR by pressing Two less than sup greater than nd less than divided by sup greater than and then vars.
Scroll down to option binompdf left parenthesis. Press Enter key.
1. If prompted, input the number of trials, the probability of success, and the number of successes. Highlight PASTE and then press Enter key.
2. If not prompted, type the number of trials, the probability of success, and the number of successes separated by commas.
Press Enter key to display the probability.

Binomial Probability Distribution

Select DISTR by pressing Two less than sup greater than nd less than divided by sup greater than and then vars.
Scroll down to option binompdf left parenthesis. Press Enter key.
1. If prompted, input the number of trials and the probability of success. Highlight PASTE and then press Enter key.
2. If not prompted, type the number of trials and the probability of success separated by a comma. Press right parenthesis.
To store the probabilities in L2, press STO→ semicolon, then second, and then Two. Press Enter key.
press STAT, select Edit from the top menu, choose Edit horizontal ellipsis, and press Enter key. See Adding Info to Lists for further help on entering your data.
Input the values 0 to n in L1 to complete the binomial distribution table.

Binomial Probability (cdf)

Select DISTR by pressing 2 less than sup greater than nd less than divided by sup greater than and then vars.
Scroll down to option binomcdf left parenthesis. Press Enter key.
1. If prompted, input the number of trials, the probability of success, and the number of successes. Highlight PASTE and then press Enter key.
2. If not prompted, type the number of trials, the probability of success, and the number of successes separated by commas.
Press Enter key 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 Two less than sup greater than nd less than divided by sup greater than and then vars.
Scroll down to χ semicolon less than sup greater than Two less than divided by sup greater than cdf left parenthesis from the menu. Press Enter key.
Input zero (the lower bound), the χ² test statistic, and the degrees of freedom separated by commas.
Press Enter key.

Right Tailed Probability (cdf)

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

Select DISTR by pressing 2 less than sup greater than nd less than divided by sup greater than and then vars.
Scroll down to χ semicolon less than sup greater than 2 less than divided by sup greater than cdf left parenthesis from the menu. Press Enter key.
Input the χ² test statistic, the upper bound, and the degrees of freedom separated by commas.

Note, if your upper bound is positive infinity, use a very large positive number such as 1E99. The symbol E is entered by pressing second and then ,.
Press Enter key.

Test for Association

Select MATRIX by either pressing MATRX or by pressing 2 less than sup greater than nd less than divided by sup greater than and thenx less than sup greater than negative 1 less than divided by sup greater than, depending on your calculator version.
select Edit from the top menu, and left square bracket A right square bracket. Press Enter key.
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 left square bracket A right square bracket of the matrix and the expected values in the second column left square bracket B right square bracket.
Press STAT, select TESTS from the top menu, and scroll down to χ²-Test. Press Enter key.
Enter left square bracket A right square bracket for Observed, and left square bracket B right square bracket for Expected. Note that matrices can be entered by pressing MATRX and selecting the appropriate matrix's name from the list.
Select Calculate and press Enter key.

Test for Goodness of Fit

press STAT, select Edit from the top menu, choose Edit horizontal ellipsis, and press Enter key.
Input the observed data in L1 and the expected values in L2. See Adding Info to Lists for further help on entering your data.
Press STAT, select TESTS from the top menu, and scroll down to χ semicolon less than sup greater than 2 less than divided by sup greater than GOF minus Test. Press Enter key.
Enter L1 for Observed, and L2 for Expected. Note that lists can be entered by pressing second followed by the number of the list. For example, second and one gives L1.

Enter the appropriate degrees of freedom (df).
Select Calculate and press Enter key.

Confidence Intervals

Proportion

Press STAT and select TESTS from the top menu, then scroll down to option One minus Propz Int. Press Enter key.
Input the number of successes, the number of observations, and the confidence level.
Select Calculate and press Enter key.

`t-`Interval

Using Summary Statistics

Press STAT and select TESTS from the top menu, then scroll down to option T Interval. Press Enter key.
Choose Stats and press Enter key.
Input the sample mean, the sample standard deviation, the sample size, and the confidence level.
Select Calculate and press Enter key.

Using Data

press STAT, select Edit from the top menu, choose Edit horizontal ellipsis, and press Enter key.
Input the data in the column labeled L1, pressing Enter key after each value. See Adding Info to Lists for further help on entering your data.
Press STAT and select TESTS from the top menu, then scroll down to option T Interval. Press Enter key.
Choose Data as the input and press Enter key.
Input the confidence level.

Note that lists can be entered by pressing second followed by the number of the list. For example, second and one gives L1. Also, the frequency of the list should be 1.
Select Calculate and press Enter key.

`z-`Interval

Using Summary Statistics

Press STAT and select TESTS from the top menu, then scroll down to option Z Interval. Press Enter key.
Choose Stats and press Enter key.
Input the population standard deviation, the sample mean, the sample size, and the confidence level.
Select Calculate and press Enter key.

Using Data

press STAT, select Edit from the top menu, choose Edit horizontal ellipsis, and press Enter key.
Input the data in the column labeled L1, pressing Enter key after each value. See Adding Info to Lists for further help on entering your data.
Press STAT and select TESTS from the top menu, then scroll down to option Z Interval. Press Enter key.
Choose Data as the input and press Enter key.
Input the population standard deviation and the confidence level.

Note that lists can be entered by pressing second followed by the number of the list. For example, second and one gives L1. Also, the frequency of the list should be 1.
Select Calculate and press Enter key.

Two Sample z-Interval

Using Summary Statistics

Press STAT and select TESTS from the top menu, then scroll down to option 2 minus Sampz Int. Press Enter key.
Choose Stats and press Enter key.
Input both population standard deviations, both sample means, both sample sizes, and the confidence level.
Select Calculate and press Enter key.

Using Data

press STAT, select Edit from the top menu, choose Edit horizontal ellipsis, and press Enter key.
Input the data for Sample 1 in the column labeled L1, pressing Enter key after each value. Input the data for Sample 2 in the column labeled L2, pressing Enter key after each value. See Adding Info to Lists for further help on entering your data.
Press STAT and select TESTS from the top menu, then scroll down to option 2 minus Sampz Int. Press Enter key.
Choose Data as the input and press Enter key.
Input both population standard deviations and the confidence level.

Note that lists can be entered by pressing second followed by the number of the list. For example, second and one gives L1. Also, the frequency for each list should be 1.
Select Calculate and press Enter key.

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

Using Summary Statistics

See t-interval, Using Summary Statistics.

Using Data

press STAT, select Edit from the top menu, choose Edit horizontal ellipsis, and press Enter key.
Input the data for Sample 1 (before data) in the column labeled L1, pressing Enter key after each value. Input the data for Sample 2 (after data) in the column labeled L2, pressing Enter key after each value. See Adding Info to Lists for further help on entering your data.
Highlight L3 and enter the formula L2 − L1 and then Enter key.

Note that lists can be entered by pressing second followed by the number of the list. For example, second and one gives L1.
Press STAT and select TESTS from the top menu, then scroll down to option T Interval. Press Enter key.
Choose Data as the input and press Enter key.
Input L3 for the List and input the confidence level. Note, the frequency of the list should be 1.
Select Calculate and press Enter key.

Two Sample `t`-Interval (Independent Samples)

Using Summary Statistics

Press STAT, select TESTS from the top menu, and scroll down to 2 minus SampTInt. Press Enter key.
Choose Stats as the input and press Enter key.
Input the sample mean, the sample standard deviation, and the sample size for sample 1 and 2. Input the confidence level.

For Pooled colon choose “Yes” when assuming the population variances are equal and choose “No” when assuming the population variances are not equal.
Select Calculate and then press Enter key 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 from the top menu, choose Edit horizontal ellipsis, and press Enter key.
1. Input the data for Sample 1 under L1, pressing Enter key after each value. See Adding Info to Lists for further help on entering your data.
2. Input the data for Sample 2 under L2, pressing Enter key after each value.
Press STAT, select TESTS from the top menu, and scroll down to 2 minus SampTInt. Press Enter key.
Choose Data as the input and press Enter key.
Input the list names where the data is stored. Note that lists can be entered by pressing second followed by the number of the list. For example, second and one gives L1.

Input the confidence level.

For Pooled colon choose “Yes” when assuming population variances are equal and choose “No” when assuming the population variances are not equal.
Select Calculate and then press Enter key 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 Proportions z-Interval

Press STAT and select TESTS from the top menu, then scroll down to option 2 minus Propz Int. Press Enter key.
Input the number of successes for both samples, the number of observations for both samples, and the confidence level.
Select Calculate and press Enter key.

Counting

Combination

Enter the number of objects.
Press MathMath and select PROB from the top menu, then choose option nCr. Press Enter key.
Enter the number of objects taken at a time. Press Enter key.
Divide 1 by the resulting number of combinations to find the probability of any single combination occurring.

Note, the resulting number of combinations can be entered by using the ANS function, which is accessed by pressing second followed by left parenthesis minus right parenthesis.

Factorial

Enter the value for which you are calculating the factorial.
Press Math and select PROB from the top menu, then choose option factorial. Press Enter key.
Press Enter key.

Permutation

Enter the number of objects.
Press Math and select PROB from the top menu, then choose option nPr. Press Enter key.
Enter the number of objects you are taking at a time.
Press Enter key.

Data Manipulation

Sorting

press STAT, select Edit from the top menu, choose Edit horizontal ellipsis, and press Enter key.
Input the data in the column labeled L1, pressing Enter key after each value. See Adding Info to Lists for further help on entering your data.
1. To sort the list in ascending order, press STAT and select Edit from the top menu, then choose option SortA left parenthesis. Press Enter key.
2. To sort the list in descending order, press STAT and select Edit from the top menu, then choose option SortD left parenthesis. Press Enter key.
Enter the name of the list to be sorted. Press Enter key.

Note that lists can be entered by pressing second followed by the number of the list. For example, second and one gives L1.
To view the sorted list, press STAT, select Edit from the top menu, choose Edit horizontal ellipsis, and press Enter key.

Descriptive Statistics

One Variable

press STAT, select Edit from the top menu, choose Edit horizontal ellipsis, and press Enter key.
Input the data in the column labeled L1, pressing Enter key after each value. See Adding Info to Lists for further help on entering your data.
Press STAT and select CALC from the top menu, then choose option 1 Var Stats. Press Enter key.
1. If prompted, verify the list entered is L1, select Calculate, and press Enter key.
2. If not prompted. Press Enter key.
  
  Note, L1 is the default list of data. If you wish to compute the descriptive statistics of another list of data, you may enter the list name by pressing second followed by the number of the list, and then press Enter key.
The values on the screen will be listed, in order, as follows.

Two Variable

Grouped Data

press STAT, select Edit from the top menu, choose Edit horizontal ellipsis, and press Enter key.
1. Input the midpoints of the intervals in the column labeled L1, pressing Enter key after each value. See Adding Info to Lists for further help on entering your data.
2. Input the frequency values in the column labeled L2.
Press STAT and select CALC from the top menu, then choose option 1 Var Stats. Press Enter key.
1. If prompted, verify the list entered is L1; for Freqlist, type L2; select Calculate; and press Enter key.
  
  Note that lists can be entered by pressing second followed by the number of the list. For example, second and Two gives L2.
2. If not prompted, type L1, L2.
  
  Note that lists can be entered by pressing second followed by the number of the list. For example, second and one gives L1.
Press Enter key.

Variance of a Discrete Random Variable

press STAT, select Edit from the top menu, choose Edit horizontal ellipsis, and press Enter key.
1. Input the x-values in the column labeled L1, pressing Enter key after each value. See Adding Info to Lists for further help on entering your data.
2. Input the probabilities in the column labeled L2.
Press STAT and select CALC from the top menu, then choose option 1 Var Stats. Press Enter key.
1. If prompted, verify the list entered is L1; for Freqlist, type L2; select Calculate; and press Enter key.
  
  Note that lists can be entered by pressing second followed by the number of the list. For example, second and Two gives L2.
2. If not prompted, type L1, L2.
  
  Note that lists can be entered by pressing second followed by the number of the list. For example, second and one gives L1.
Press Enter key.
Note, the standard deviation is returned in the output after the label σ semicolon x, and the variance can be found by squaring this value.

TI-Calculator Variance of a Discrete Random Variable step 6a

TI-Calculator Variance of a Discrete Random Variable step 6b

Weighted Mean

press STAT, select Edit from the top menu, choose Edit horizontal ellipsis, and press Enter key.
1. Input the weight values in the column labeled L1, pressing Enter key after each value. See Adding Info to Lists for further help on entering your data.
2. Input the frequency values in the column labeled L2.
Press STAT and select CALC from the top menu, then choose option 1 Var Stats. Press Enter key.
1. If prompted, verify the list entered is L1; for Freqlist, type L2; select Calculate; and press Enter key.
  
  Note that lists can be entered by pressing second followed by the number of the list. For example, second and Two gives L2.
2. If not prompted, type L1, L2.
  
  Note that lists can be entered by pressing second followed by the number of the list. For example, second and one gives L1.
Press Enter key.
Note, the standard deviation is returned in the output after the label σ semicolon x, and the variance can be found by squaring this value.

`F`-Distribution

`F`-Probability (cdf)

Select DISTR by pressing 2 less than sup greater than nd less than divided by sup greater than and then vars.
Scroll down to Fcdf left parenthesis. Press Enter key.
1. If prompted, input the lower F value, the upper F value, the numerator degrees of freedom, and the denominator degrees of freedom. Highlight PASTE and press Enter key.
  
  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 negative 1E99 or 1E99. The symbol E is entered by pressing second and then ,.
2. If not prompted, type the lower F value, the upper F value, the numerator degrees of freedom, and the denominator degrees of freedom separated 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 such as negative 1E99 or 1E99. The symbol E is entered by pressing second and then ,.
Press Enter key.

Graphs

Bar Charts

press STAT, select Edit from the top menu, choose Edit horizontal ellipsis, and press Enter key.
Enter your category data into list L1 and enter your frequency data into list L2. See Adding Info to Lists for further help on entering your data.
Choose STAT PLOT by pressing second and then Y equals.
Highlight a plot and then press Enter key.
Select On and the bar chart icon, which is the third option in the second row. For X list, enter L1. For Freq, enter L2.

Note that lists can be entered by pressing second followed by the number of the list. For example, second and one gives L1.
Press Graph to display the bar chart. You can resize the graph by pressing Window to adjust the horizontal and vertical scales or by pressing Zoom and then choosing Zoom Stat.

Box Plot

press STAT, select Edit from the top menu, choose Edit horizontal ellipsis, and press Enter key.
Input the data into a list, pressing Enter key after each value. See Adding Info to Lists for further help on entering your data.
Choose STAT PLOT by pressing second and then Y equals.
Highlight a plot and then press Enter key.
Select On.
1. If you would like outliers to be plotted as points beyond the whiskers of the box plot, select the box plot icon that is the fourth option in the second row.
2. If you would like the whiskers of the box plot to extend to all points (even outliers), select the box plot icon that is the fifth option in the second row.
For X list, enter the name of the list where the data is stored. For Freq, enter one.

Note that lists can be entered by pressing second followed by the number of the list. For example, second and one gives L1.
Press Graph to display the box plot. You can resize the graph by pressing Window to adjust the horizontal and vertical scales or by pressing Zoom and then choosing Zoom Stat.

Histogram

press STAT, select Edit from the top menu, choose Edit horizontal ellipsis, and press Enter key.
Input the data into a list, pressing Enter key after each value. See Adding Info to Lists for further help on entering your data.
Choose STAT PLOT by pressing second and then Y equals.
Highlight a plot and then press Enter key.
Select On and the histogram icon, which is the third option in the second row. For X list, enter the name of the list where the data is stored. For Freq, enter one.

Note that lists can be entered by pressing second followed by the number of the list. For example, second and one gives L1.
Press 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 choosing Zoom Stat.

Line Graph

press STAT, select Edit from the top menu, choose Edit horizontal ellipsis, and press Enter key.
Input the data into lists, pressing Enter key after each value. See Adding Info to Lists for further help on entering your data.
Choose STAT PLOT by pressing second and then Y equals.
Highlight a plot and then press Enter key.
Select On and the line graph icon, which is the second option in the second row. For X list, enter the name of the list where the data to be graphed along the horizontal axis is stored. For Y list, enter the name of the list where the data to be graphed along the vertical axis is stored.

Note that lists can be entered by pressing second followed by the number of the list. For example, second and one gives L1.
Press Graph to display the line graph. You can resize the graph by pressing Window to adjust the horizontal and vertical scales or by pressing Zoom and then choosing Zoom Stat.

Normal Probability Plot

press STAT, select Edit from the top menu, choose Edit horizontal ellipsis, and press Enter key.
Input the data into lists, pressing Enter key after each value. See Adding Info to Lists for further help on entering your data.
Choose STAT PLOT by pressing second and then Y equals.
Highlight a plot and then press Enter key.
Select On and the normal probability plot icon, which is the sixth option in the second row. For Data List, enter the name of the list where the data to be graphed along the horizontal axis is stored. For Data Axis, select X.

Note that lists can be entered by pressing second followed by the number of the list. For example, second and one gives L1.
Press Graph to display the line graph. You can resize the graph by pressing Window to adjust the horizontal and vertical scales or by pressing Zoom and then choosing Zoom Stat.

Pareto Charts

press STAT, select Edit from the top menu, choose Edit horizontal ellipsis, and press Enter key.
Enter your category data into list L1 and enter your frequency data into list L2. See Adding Info to Lists for further help on entering your data.
Press STAT and select Edit from the top menu, then choose option SortD left parenthesis. Press Enter key.
Enter L2. Press Enter key.

Note that lists can be entered by pressing second followed by the number of the list. For example, second and Two gives L2.
Choose STAT PLOT by pressing second and then Y equals.
Highlight a plot and then press Enter key.
Select On and the bar chart icon, which is the third option in the second row. For X list, enter L1. For Freq, enter L2.
Press Graph to display the bar chart. You can resize the graph by pressing Window to adjust the horizontal and vertical scales or by pressing Zoom and then choosing Zoom Stat.

Scatterplot

press STAT, select Edit from the top menu, choose Edit horizontal ellipsis, and press Enter key.
Enter x-coordinate data into list L1 and enter y-coordinate data into list L2. See Adding Info to Lists for further help on entering your data.
Choose STAT PLOT by pressing second and then Y equals.
Highlight a plot and then press Enter key.
Select On and the scatterplot icon, which is the first option in the second row. For X list, enter L1. For Y list, enter L2.

Note that lists can be entered by pressing second followed by the number of the list. For example, second and one gives L1.
Press Graph to display the scatterplot. You can resize the graph by pressing Window to adjust the horizontal and vertical scales or by pressing Zoom and then choosing Zoom Stat.

Time Series

See Line Graph.

Hypergeometric Distribution

Hypergeometric Distribution

See Combination.

Hypothesis Testing

One Proportion `z`-Test

Press STAT, select TESTS from the top menu, and scroll down to 1 minus Prop ZTest. Press Enter key.
Input the proportion for the null hypothesis, the success count in the sample, and the sample size. Highlight the alternative hypothesis and press Enter key.
Select Calculate and press Enter key to observe the results of the test.

z-Test

Using Summary Statistics

Press STAT, select TESTS from the top menu, and scroll down to Z minus Test. Press Enter key.
Choose Stats as the input and press Enter key.
Input the mean for the null hypothesis, the population standard deviation, the sample mean, and the sample size. Highlight the alternative hypothesis and press Enter key.
Select Calculate and then press Enter key to observe the results of the test.

Using Data

press STAT, select Edit from the top menu, choose Edit horizontal ellipsis, and press Enter key.
Input the data into a list, pressing Enter key after each value. See Adding Info to Lists for further help on entering your data.
Press STAT, select TESTS from the top menu, and scroll down to Z minus Test. Press Enter key.
Choose Data as the input and press Enter key.
Input the mean for the null hypothesis, the population standard deviation, and the list name where the data is stored. Highlight the alternative hypothesis and press Enter key.

Note that lists can be entered by pressing second followed by the number of the list. For example, second and one gives L1.
Select Calculate and then press Enter key to observe the results of the test.

t-Test

Using Summary Statistics

Press STAT, select TESTS from the top menu, and scroll down to T minus Test. Press Enter key.
Choose Stats as the input and press Enter key.
Input the mean for the null hypothesis, the sample mean, the sample standard deviation, and the sample size. Highlight the alternative hypothesis and press Enter key.
Select Calculate and then press Enter key to observe the results of the test.

Using Data

press STAT, select Edit from the top menu, choose Edit horizontal ellipsis, and press Enter key.
Input the data into a list, pressing Enter key after each value. See Adding Info to Lists for further help on entering your data.
Press STAT, select TESTS from the top menu, and scroll down to T minus Test. Press Enter key.
Choose Data as the input and press Enter key.
Input the mean for the null hypothesis and the list name where the data is stored. Highlight the alternative hypothesis and press Enter key.

Note that lists can be entered by pressing second followed by the number of the list. For example, second and one gives L1.
Select Calculate and then press Enter key to observe the results of the test.

Two Proportion z-Test

Press STAT, select TESTS from the top menu, and scroll down to 2 minus PropZTest. Press Enter key.
Input the success count and the sample size for sample 1 and 2. Highlight the alternative hypothesis and press Enter key.
Select Calculate and press Enter key to observe the results of the test.

Two Sample `t`-Test (Independent Samples)

Using Summary Statistics

Press STAT, select TESTS from the top menu, and scroll down to 2 minus SampTTest. Press Enter key.
Choose Stats as the input and press Enter key.
Input the sample mean, the sample standard deviation, and the sample size for sample 1 and 2. Highlight the alternative hypothesis and press Enter key.

For Pooled colon choose “Yes” when assuming the population variances are equal and choose “No” when assuming the population variances are not equal.
Select Calculate and then press Enter key 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 from the top menu, choose Edit horizontal ellipsis, and press Enter key.
1. Input the data for Sample 1 under L1, pressing Enter key after each value. See Adding Info to Lists for further help on entering your data.
2. Input the data for Sample 2 under L2, pressing Enter key after each value.
Press STAT, select TESTS from the top menu, and scroll down to 2 minus SampTTest. Press Enter key.
Choose Data as the input and press Enter key.
Input the list names where the data is stored. Note that lists can be entered by pressing second followed by the number of the list. For example, second and one gives L1.

Highlight the alternative hypothesis and press Enter key.

For Pooled colon choose “Yes” when assuming population variances are equal and choose “No” when assuming the population variances are not equal.
Select Calculate and then press Enter key 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)

Using Summary Statistics

See t-Test, using Summary Statistics.

Using Data

press STAT, select Edit from the top menu, choose Edit horizontal ellipsis, and press Enter key.
Input the data for Sample 1 (before data) in the column labeled L1, pressing Enter key after each value. Input the data for Sample 2 (after data) in the column labeled L2, pressing Enter key after each value. See Adding Info to Lists for further help on entering your data.
Highlight L3 and enter the formula L2 − L1 and then Enter key.

Note that lists can be entered by pressing second followed by the number of the list. For example, second and one gives L1.
Press STAT and select TESTS from the top menu, then scroll down to option T minus Test. Press Enter key.
Choose Data as the input and press Enter key.
Input the mean for the null hypothesis and the list name where the data is stored. Highlight the alternative hypothesis and press Enter key.

Note that lists can be entered by pressing second followed by the number of the list. For example, second and Three gives L3.
Select Calculate and press Enter key to observe the results of the test.

Two Sample `z`-Test

Using Summary Statistics

Press STAT, select TESTS from the top menu, and scroll down to 2 minus SampZTest. Press Enter key.
Choose Stats as the input and press Enter key.
Input the population standard deviation, the sample mean, and the sample size for each sample. Highlight the alternative hypothesis and press Enter key.
Select Calculate and then press Enter key to observe the results of the test.

Using Data

press STAT, select Edit from the top menu, choose Edit horizontal ellipsis, and press Enter key.
1. Input the data for Sample 1 under L1, pressing Enter key after each value. See Adding Info to Lists for further help on entering your data.
2. Input the data for Sample 2 under L2, pressing Enter key after each value.
Press STAT, select TESTS from the top menu, and scroll down to 2 minus SampZTest. Press Enter key.
Choose Data as the input and press Enter key.
Input the population standard deviation for both populations, and the list names where the data is stored. Highlight the alternative hypothesis and press Enter key.

Note that lists can be entered by pressing second followed by the number of the list. For example, second and one gives L1.
Select Calculate and then press Enter key to observe the results of the test.

Two Sample `F`-Test

Using Summary Statistics

Press STAT, select TESTS from the top menu, and scroll down to 2 minus SampFTest. Press Enter key.
Choose Stats as the input and press Enter key.
Input the sample standard deviation and the sample size for each sample. Highlight the alternative hypothesis and press Enter key.
Select Calculate and then press Enter key to observe the results of the test.

Using Data

press STAT, select Edit from the top menu, choose Edit horizontal ellipsis, and press Enter key.
1. Input the data for Sample 1 under L1, pressing Enter key after each value. See Adding Info to Lists for further help on entering your data.
2. Input the data for Sample 2 under L2, pressing Enter key after each value.
Press STAT, select TESTS from the top menu, and scroll down to 2 minus SampFTest. Press Enter key.
Choose Data as the input and press Enter key.
Input the list names where the data is stored. Highlight the alternative hypothesis and press Enter key.

Note that lists can be entered by pressing second followed by the number of the list. For example, second and one gives L1.
Select Calculate and then press Enter key to observe the results of the test.

Normal Distribution

Inverse Normal

Select DISTR by pressing 2 less than sup greater than nd less than divided by sup greater than and then vars.
Scroll down to invNorm. Press Enter key.
1. If prompted, input the area, the mean, and the standard deviation. Highlight "LEFT", "CENTER", or "RIGHT", depending on whether you would like the z-value(s) with the given area to the left, center, or right, and press Enter key. Highlight PASTE and press Enter key.
2. If not prompted, type the area to the left of z, the mean, and the standard deviation separated by commas.
  
  Note, if given the area to the right of z, subtract that value from 1.
Press Enter key.

Normal Probability (cdf)

Select DISTR by pressing 2 less than sup greater than nd less than divided by sup greater than and then vars.
Scroll down to normalcdf. Press Enter key.
1. If prompted, input the lower x or z value, the upper x or z value, the mean, and the standard deviation. Highlight PASTE and press Enter key.
  
  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 negative 1E99 or 1E99. The symbol E is entered by pressing second and then ,.
2. If not prompted, type the lower x or z value, the upper x or z value, the mean, and the standard deviation separated 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 such as negative 1E99 or 1E99. The symbol E is entered by pressing second and then ,.
Press Enter key.

Normal Probability Graph

To properly view the graph, you may need to first adjust the window. Press WINDOW.
1. Recommended bounds for Xmin and Xmax are ±3σ with Xscl = σ.
2. Let Ymin = -0.1, and Ymax = 1 with Yscl = 0.1.
Select DISTR by pressing 2 less than sup greater than nd less than divided by sup greater than and then vars.
Select DRAW from the top menu and scroll down to ShadeNorm left parenthesis. Press Enter key.
1. If prompted, input the lower x or z value, the upper x or z value, the mean, and the standard deviation. Select DRAW.
  
  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 negative 1E99 or 1E99. The symbol E is entered by pressing second and then ,.
2. If not prompted, type the lower x or z value, the upper x or z value, the mean, and the standard deviation separated 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 such as negative 1E99 or 1E99. The symbol E is entered by pressing second and then ,.
Press Enter key.

Test for Normality

See Normal Probability Plot.
1. The data is likely normally distributed, if the points on the plot cluster closely around a straight line.
2. The data is likely not normally distributed, if the points deviate significantly from a straight line.

Poisson Distribution

Poisson Probability (cdf)

Select DISTR by pressing 2 less than sup greater than nd less than divided by sup greater than and then vars.
Scroll down to option poissoncdf left parenthesis. Press Enter key.
1. If prompted, input the mean and the number of successes. Highlight PASTE and press Enter key.
2. If not prompted, type the mean and the number of successes separated by a comma.
Press Enter key to display the cumulative probability.

Poisson Probability (pdf)

Select DISTR by pressing 2 less than sup greater than nd less than divided by sup greater than and then vars.
Scroll down to option poissonpdf left parenthesis. Press Enter key.
1. If prompted, input the mean and the number of successes. Highlight PASTE and press Enter key.
2. If not prompted, type the mean and the number of successes separated by a comma.
Press Enter key to display the probability.

Poisson Probability Distribution

press STAT, select Edit from the top menu, choose Edit horizontal ellipsis, and press Enter key. See Adding Info to Lists for further help on entering your data.
Input the values 0 to n in L1.
Press QUIT by pressing second and then MODE.
Select DISTR by pressing 2 less than sup greater than nd less than divided by sup greater than and then vars.
Scroll down to option poissonpdf left parenthesis. Press Enter key.
1. If prompted, input the mean. Enter L1 as the probability of success by pressing second and then one. Highlight PASTE and then press Enter key.
2. If not prompted, type the mean, a comma, and L1.
  
  Note, to type L1 press second and then one.
Then store the probabilities in L2, press STO→ semicolon, then 2 less than sup greater than nd less than divided by sup greater than, and then Two. Press Enter key.
To view the distribution table, press STAT, select Edit from the top menu, choose Edit horizontal ellipsis, and press Enter key.

Regression

Confidence Interval for Slope

(Not available on all TI models)

press STAT, select Edit from the top menu, choose Edit horizontal ellipsis, and press Enter key. See Adding Info to Lists for further help on entering your data.
Enter the x-values into L1 (pressing Enter key after each value), and the y-values into L2.
Press STAT, select TESTS from the top menu, and scroll down to LinRegTInt. Press Enter key.
1. Verify X list is L1, Y list is L2, and Freq is one.
  
  Note that lists can be entered by pressing second followed by the number of the list. For example, second and one gives L1.
2. Input the confidence level.
3. For Reg EQ, enter Y1 by pressing vars, selecting Y minus Vars from the top menu, scrolling down to Function horizontal ellipsis, and pressing Enter key. Choose Y1 from the list and press Enter key.
4. Highlight Calculate.
Press Enter key.

Hypothesis Testing for Slope Coefficient

See Calculating the P-value.

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 second and then zero.
Scroll down to DiagnosticOn. Press Enter key.
Press Enter key again and observe that the screen says "Done".
Follow the instructions for Simple Linear Regression.

Simple Linear Regression

Finding the Regression Line

press STAT, select Edit from the top menu, choose Edit horizontal ellipsis, and press Enter key. See Adding Info to Lists for further help on entering your data.
Enter the x-values into L1 (pressing Enter key after each value), and the y-values into L2.
Press STAT, select CALC from the top menu, and scroll down to Linreg left parenthesis a plus b x right parenthesis. Press Enter key.

Note, Linreg left parenthesis ax plus b right parenthesis is an alternate option. It is mathematically identical and differs only in the order in which the answer is written.
1. If prompted, for X list, type L1; and for Y list, type L2. Note that lists can be entered by pressing second followed by the number of the list. For example, second and one gives L1.
  
  To store the regression equation for graphing, in the Store RegEQ field, press vars, select Y minus Vars from the top menu, scroll down to Function horizontal ellipsis, and press Enter key. Choose a y-variable from the list and press Enter key.
  
  Highlight Calculate.
2. If not prompted, type L1, a comma, L2, a comma, and Y1.
  
  Note that lists can be entered by pressing second followed by the number of the list. For example, second and one gives L1.
  
  Also note, to enter Y1, press vars, select Y minus Vars from the top menu, scroll down to Function horizontal ellipse, and press Enter key. Choose a y-variable from the list and press Enter key.
Press Enter key. The linear regression equation may also be viewed by pressing Y equals.

Note: If Diagnostics are OFF, only the equation and values of a and b will be displayed. See Correlation Coefficient and Coefficient of Determination for instructions to turn Diagnostics ON.

Calculating the P-value

After finding and storing the regression line, press STAT, select TESTS from the top menu, and scroll down to LinRegTTest. Press Enter key.
Verify X list is L1, Y list is L2, and Freq is one. Note that lists can be entered by pressing second followed by the number of the list. For example, second and one gives L1.

Verify not equal to zero is selected for less than var greater than beta less than divided by var greater than ampersand less than var greater than p less than divided by var greater than .

For Reg EQ, enter Y1 by pressing vars, selecting Y minus Vars from the top menu, scrolling down to Function horizontal ellipsis, and pressing Enter key. Choose Y1 from the list and press Enter key.

Highlight Calculate.
Press Enter key.

Standard Error of Estimate

press STAT, select Edit from the top menu, choose Edit horizontal ellipsis, and press Enter key. See Adding Info to Lists for further help on entering your data.
Enter the x-values into L1 (pressing Enter key after each value), and the y-values into L2.
Press STAT, select TESTS from the top menu, and scroll down to LinRegTTest. Press Enter key.
Verify X list is L1, Y list is L2, and Freq is one. Note that lists can be entered by pressing second followed by the number of the list. For example, second and one gives L1.

Verify not equal to zero is selected for less than var greater than beta less than divided by var greater than ampersand less than var greater than p less than divided by var greater than.

Enter the regression equation into Reg EQ if you have already calculated it. If not, you may leave this blank. To enter Y1, press vars, select Y minus Vars from the top menu, scroll down to Function horizontal ellipsis, and press Enter key. Choose Y1 from the list and press Enter key.

Highlight Calculate.
Press Enter key. The standard error of estimate is s.

Sampling

Random Samples

Random Integer Samples

Press Math, select PROB from the top menu, and scroll down to randInt left parenthesis. Press Enter key.
1. If prompted, input an integer lower bound of desired sample values, an integer upper bound of desired sample values, and the desired sample size.
  
  Highlight PASTE and press Enter key.
2. If not prompted, type an integer lower bound of desired sample values, an integer upper bound of desired sample values, and the desired sample size, separated by commas.
Press Enter key. The random integers are listed on the screen.
To store the sample in L1, press STO→ semicolon, then second, and then one. Press Enter key.

Random Real Number Samples

Press Math, select PROB from the top menu, and scroll down to rand. Press Enter key.
Type left parenthesis, the desired sample size, and right parenthesis. Press Enter key.
To store the sample in L1, press STO→ semicolon, then second, and then one. Press Enter key.
To adjust the range of the values in your sample, you will need to create a formula of the form a asterisk times L1 plus b, where b is the minimum value of your desired sample and a is the range of your desired sample. The value of a can be computed by subtracting the minimum value of your desired sample from the maximum value of your desired sample.
1. press STAT, select Edit from the top menu, choose Edit horizontal ellipsis, and press Enter key.
2. Highlight L2, enter the formula a asterisk times L1 plus b, and press Enter key.
  
  Note that lists can be entered by pressing second followed by the number of the list. For example, second and one gives L1.

`t`-Distribution

Inverse `t`

Select DISTR by pressing 2 less than sup greater than nd less than divided by sup greater than and then vars.
Scroll down to invT left parenthesis. Press Enter key.
1. If prompted, input the area of the left tail and the degrees of freedom. Highlight PASTE and press Enter key.
2. If not prompted, type the area of the left tail and the degrees of freedom separated by a comma.
Press Enter key.

`t`-Probability (cdf)

Select DISTR by pressing 2 less than sup greater than nd less than divided by sup greater than and then vars.
Scroll down to tcdf left parenthesis. Press Enter key.
1. If prompted, input the lower t value, the upper t value, and the degrees of freedom. Highlight PASTE and press Enter key.
  
  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 negative 1E99 or 1E99. The symbol E is entered by pressing second and then ,.
2. If not prompted, type the lower t value, the upper t value, and the degrees of freedom separated 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 such as negative 1E99 or 1E99. The symbol E is entered by pressing second and then ,.
Press Enter key.