G Notes for the TI-83, 83+, 84, 84+ Calculators - Statistics | OpenStax (2024)

Sample Data

The following data are real. The percent of declared ethnic minority students at De Anza College for selected years from 1970–1995 is indicated in the following table.

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

To enter data and perform linear regression

1. ON Turns calculator on.
   

2. Before accessing this program, be sure to turn off all plots.

   • Access graphing mode.
     , [STAT PLOT].

   • Turn off all plots.
     ,.

3. Round to three decimal places.

   • Access the mode menu.
     , [STAT PLOT].

   • Navigate to <Float> and then to the right until you reach <3>.
     .

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

4. Enter statistics mode and clear lists [L1] and [L2], as described previously.
   ,.

5. Enter editing mode to insert values for x and y.
   ,.

6. Enter each value. Press to continue.

To display the correlation coefficient

1. Access the catalog.
   , [CATALOG].

2. Arrow down and select <DiagnosticOn>.
   ... , ,.

3. $r$ and$r^2$ will be displayed during regression calculations.

4. Access linear regression.
   .

5. Select the form of y = a + bx.
   ,.

The display will show the following information

LinReg

• y = a + bx
• a = –3176.909
• b = 1.617
• r² = 0.924
• r = 0.961

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

• y = –3176.909 + 1.617x
• % = –3176.909 + 1.617 (year #)

The correlation coefficient is r = 0.961.

To see the scatter plot

1. Access graphing mode.
   , [STAT PLOT].

2. Select <1:Plot 1> To access plotting - first graph.
   

3. Navigate and select <ON> to turn on <1:Plot 1>.
   <ON>.

4. Navigate to the first picture.

5. Select the scatter plot.
   

6. Navigate to <Xlist>.
7. If [L1] is not selected, press , then [L1] to select it.

8. Confirm that the data values are in [L1].
   <ON>,.

9. Navigate to <Ylist>.

10. Select that the frequencies are in [L2].
    , [L2] ,

11. Go back to access other graphs.
    , [STAT PLOT]

12. Use the arrows to turn off the remaining plots.
13. Access window mode to set the graph parameters.
    
    • $X_{\min }=1970$
    • $X_{\max }=2000$
    • $X_{scl}=10$ (spacing of tick marks on x-axis)
    • $Y_{\min }=-0.05$
    • $Y_{\max }=60$
    • $Y_{scl}=10$ (spacing of tick marks on y-axis)
    • $X_{res}=1$
14. Be sure to deselect or clear all equations before graphing, using the instructions above.
15. Press the graph button to see the scatter plot.

To see the regression graph

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

2. Access the vars menu and navigate to <5: Statistics>.
   ,.

3. Navigate to <EQ>.

4. <1: RegEQ> contains the regression equation which will be entered in Y1.
   

5. 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

1. Access the list. <RESID> will be an item on the menu. Navigate to it.
   , [LIST], then <RESID>.

2. Press enter twice to view the list of residuals. Use the arrows to select them.
   ,.

3. 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
   • $\sum _{}^{}{\mathrm{residual}}^2$

4. Store the residuals in [L3].
   , , [L3] ,.

5. Calculate the$\frac{{\mathrm{(residual)}}^2}{n-2}$. Note that$n-2=8$.
   , [L3] , , , then.

6. Store this value in [L4].
   , , [L4] ,.

7. Calculate the critical value using the equation above.
   , , , , , [V] , , [LIST] , , , , [L4] , , , then.

8. Verify that the calculator displays 7.642669563. This is the critical value.
9. 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-valuesThere 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.

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

Poisson Distribution

• poissonpdf(λ,x) corresponds to P(X = x)
• poissoncdf(λ,x) corresponds to 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(x,μ,σ) yields a probability density function value, only useful to plot the normal curve, in which case "x" is the variable
• normalcdf(left bound, right bound, μ, σ) corresponds to P(left bound < X < right bound)
• normalcdf(left bound, right bound) corresponds to P(left bound < Z < right bound) – standard normal
• invNorm(p,μ,σ) yields the critical value, k: P(X < k) = p
• invNorm(p) yields the critical value, k: P(Z < k) = p for the standard normal

Student's t-Distribution

• tpdf(x,df) yields the probability density function value, only useful to plot the student-t curve, in which case "x" is the variable)
• tcdf(left bound, right bound, df) corresponds to P(left bound < t < right bound)

Chi-square Distribution

• Χ2pdf(x,df) yields the probability density function value, only useful to plot the chi² curve, in which case "x" is the variable
• Χ2cdf(left bound, right bound, df) corresponds to P(left bound < Χ² < right bound)

F Distribution

• Fpdf(x,dfnum,dfdenom) yields the probability density function value, only useful to plot the F curve, in which case "x" is the variable
• Fcdf(left bound,right bound,dfnum,dfdenom) corresponds to 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.

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 σs are known.
• 2-SampTTest is the hypothesis test for two independent means when both σs are unknown.
• 1-PropZTest is the hypothesis test for a single proportion.
• 2-PropZTest is the hypothesis test for two proportions.
• Χ2-Test is the hypothesis test for independence.
• Χ2GOF-Test is the hypothesis test for goodness-of-fit (TI-84+ only).
• LinRegTTEST is the hypothesis test for Linear Regression (TI-84+ only).