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Directions for TI-83/84 PLUS Unit I Part I Exploring and Understanding Data Clearing Data STAT > 1:EDIT > highlight the list name at the top > CLEAR > ENTER. Entering Data STAT > 1:EDIT > type each number > ENTER. Ordering data STAT> 2:SortA( list ) Sorts list in ascending order. Link other lists to that list to keep data together. Or you can use SortD to sort in descending order. Organizing lists STAT>5:SetUpEditor[ listname1, …, listname20 ] Puts lists in order, creates new ones if listed, without names orders L1 - L6 and erases others. Graphs 1. Stem-and-leaf STAT > 2:SortA( > enter your list Use the sorted data to construct the stem-and-leaf graph by hand. 2. Histograms 2nd Y: STAT PLOTS > ENTER > ENTER (to turn the STAT PLOT on) > Appropriate graph needs to be highlighted. Xlist: name of list where data is > Freq: 1 > ZOOM 9 To adjust bins: Window > Xmin = value below your lowest value, Xmax = value above your largest value, Xscl = bin width, Ymin = -1, Ymax = value above your highest frequency, Yscl = 1 (depends on your frequency numbers), Xres =1 3. Boxplots Enter your data into list 1, list 2, and/or list 3 > 2nd Y = : StatPlots > ENTER for the first StatPlot > ENTER to turn the StatPlot on > Type: arrow over to the first box plot > ENTER > the List you want for the Xlist; Freq: 1 >Repeat the process for each list if you are doing more than one boxplot >ZoomStat (Zoom 9) By choosing the first boxplot, you will get modified boxplots. These boxplots indicate outliers. Data which are 1.5 times the IQR away from the quartiles Q1 or Q3 are called outliers. You can do a trace and notice which numbers are indicated as you move along the bars. Summary statistics STAT > CALC > 1:1-Var Stats > ENTER > 2nd 1 to insert L1 > ENTER. Normal Distributions 2nd VARS: DISTR, 2:normalcdf( lower bound, upper bound, [mean, standard deviation] ). Returns the normal probability (area) between the bounds. 2nd VARS: DISTR, 3:invNorm( area, [mean, standard deviation] ) Returns the x-score for the given area (probability). Normal Probability Plot Stat Plot>select the last plot of the Types>specify your data list > Zoom 9. This is the best way to tell if your data can be modeled well by a normal model. Make sure the other graphs are turned off. Part II Exploring Relationships Between Variables Linear Regressions Turn diagnostics on. 2nd> 0: CATALOG >scroll down to DiagnosticOn > Enter > Enter Now your calculator is set for all the regression problems you will do. You don’t need to do this step again unless you turn off the Diagnostics. This “turns on” the r and r-squared values when you do regression. For regression you need two lists – they must be exactly the same length or you will get a dimension error. STAT > CALC >4: LinReg(ax+b) > ENTER > enter your two lists (i.e. 2nd 1: L1 > comma > 2nd 2: L2 > comma > VARS > Y-VARS > 1: Function > 1: Y1 > ENTER You will have your regression line entered in Y1 in the Y=. Plotting the points 2nd Y= : STAT PLOTS > 1: Plot 1…On > we want the first plot Check the lists and make certain they agree with the ones you used Now press ZOOM 9: ZoomStat. You should see the scatterplot and the regression line. To find Residuals: Stat > 1:Edit > Enter > Scroll over on the list names at the top of the screen and you will find an “empty” list after list six > Highlight on that empty space > LIST (2nd Stat) > RESID >ENTER You should now have a residual list and the calculator will calculate the residuals for each of your x values when you do a regression. Unit II Part III Gathering Data Generate random data MATH > PRB > 5: randInt( low, high, number of random numbers desired) > ENTER Returns random integers between the bounds, inclusive. MATH>PRB>7:randBin( number of trials, probability of success, [simulations] ) Returns the number of successes in a binomial simulation. Part IV Randomness and Probability Expected Value Enter data unto L1 and probabilities into L2. STAT > CALC > 1:1-Var Stats > ENTER > 2nd 1 to insert L1 > comma > 2nd 2 to insert L2 > ENTER. Binomial Distributions DISTR, A: binompdf( number of trials, probability of success, [number of successes] ) Returns the binomial probability at X. If no argument, x, is used, it returns all probabilities for x values from 0 to n. DISTR, B: binomcdf( number of trials, probability of success, [number of successes] ) Returns the cumulative binomial probabilities from 0 to x. Unit III Part V From the Data at Hand To the World at Large Confidence interval for a proportion STAT > TESTS > A: 1-PropZInt > x: the number of successes (these should be counts not percents), n: total number, C-Level: confidence level desired > Calculate Hypothesis test for a proportion STAT >TESTS > 5: 1-PropZTest > Enter > Type in the appropriate values (Beware: When you enter the value of x, you must use counts, not percents) > Select alternative > Enter > Select Calculate or Draw (if you select Draw, be certain you don’t have other graphs turned on) You sometimes get a nicer value for the p-value in Calculate. Confidence Interval for the difference between two proportions STAT > TESTS > B: 2-PropZInt > x1: number of successes in the first group (this number must be a count), n1: total number in the first group, x2: number of successes in the second group (this number must be a count), n2: total number in the second group > C-Level: desired confidence level > Calculate Hypothesis test for the difference between two proportions STAT > TESTS > 6: 2-PropZTEST > type in appropriate values x1: number of successes in the first group, n1: total number in the first group, x2: number of successes in the second group, n2: total number in the second group > the alternative hypothesis > either Calculate or Draw (if you select Draw, be certain you don’t have other graphs turned on) Part VI Learning About the World Confidence interval for a mean With statistics STAT > TESTS > 8: TInterval > Stats > ENTER > Enter the appropriate values for the sample mean, sample standard deviation, number in sample > Select C-Level > Calculate With data Level > Calculate STAT > TESTS > 8: TInterval > Data > List > Select C- Hypothesis test for the mean With statistics STAT > TESTS > 2: T-Test > Stats > Enter > Type in the appropriate values > Select alternative > Enter > Select Calculate or Draw (if you select Draw, be certain you don’t have other graphs turned on) > Enter You sometimes get a “nicer” value for the p-value in Calculate. With data STAT > TESTS > 2: T-Test > Data > Enter > Type in the value for the mean from the null hypothesis and indicate the list containing your data > Select alternative > Enter > Select Calculate or Draw (if you select Draw, be certain you have all other graphs turned off) > Enter 2nd VARS: DISTR, 5:tcdf( lower bound, upper bound, d.f.) Returns the t-distribution probability between the bounds with given degrees of freedom. Confidence intervals for the difference between two means – independent samples With statistics STAT > TESTS > 0: 2-SampTInt> Stats > ENTER > type in the appropriate values for the sample mean, x1, sample standard deviation, S x 1 , the sample size, n1. Then do the same for the second sample > C-Level > Pooled: No > select either Calculate > ENTER With data STAT > TESTS > 0: 2-SampTInt > Data > Make sure the lists are the correct lists that contain your data > Freq1: 1, Freq2: 1 > C-Level> Pooled: No > select either Calculate > ENTER Hypothesis test for the difference between two means – independent samples With statistics STAT > TESTS > 4: 2-SampTTest > Stats > ENTER > type in the appropriate values for the sample mean, x1, sample standard deviation, S x 1 , the sample size, n1. Then do the same for the second sample > select the appropriate alternative hypothesis > Pooled: No > select either Calculate or Draw (remember you need to have all other graphs turned off if you select Draw) > ENTER With data STAT > TESTS > 4: 2-SampTTest > Data > ENTER > Make sure the lists are the correct lists that contain your data > Freq1: 1, Freq2: 1 > select the appropriate alternative hypothesis > Pooled: No > select either Calculate or Draw (remember you need to have all other graphs turned off if you select Draw) > ENTER Confidence intervals for the difference between two means – paired data With statistics STAT > TESTS > 8: TInterval > Stats > Type the appropriate values for your differences > mean, standard deviation and total > CLevel > Calculate >Enter With data Enter the data into two lists like L1 and L2. Move the cursor to the top of a new list like L3 so that list number is highlighted. Type L1L2 > ENTER > STAT > TESTS > 8: T Interval > Data > Enter > List: should be your list with differences possibly L3 > Calculate > Enter Hypothesis test for the difference between two means – Paired data With statistics See Hypothesis test for the mean. Use the values for the differences in your two sets of data. With data Enter the data into two lists like L1 and L2. Move the cursor to the top of a new list like L3 so that list number is highlighted. Type L1L2 > ENTER > STAT > TESTS > 2: T-Test > Data > The hypothesis mean is 0 > List: this is the list of the differences > Select the correct alternative hypothesis > select either Calculate or Draw (remember you need to have all other graphs turned off if you select Draw) > ENTER Part VII Inference When Variables Are Related Independence and Homogeneity MATRIX > EDIT > 1: [A] > ENTER > Enter the number of rows and columns of the matrix > ENTER > Enter the cell entries for the observed matrix > 2nd MODE (QUIT) > STAT > TESTS > C: 2 Test > Calculate or Draw > ENTER Goodness of Fit STAT > Enter the observed data in L1 > Enter the expected values in L2 > STAT > TESTS > D: 2 GOF Test > Enter degrees of freedom > select either calculate or draw > ENTER DISTR, 7: 2 cdf( lower bound, upper bound, degrees of freedom) Returns the Chi-squared probability between the bounds with given degrees of freedom.