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The Power of Technology: Using the TI-83/84 and Excel in Statistics Keisha Brown Perimeter College at Georgia State University [email protected] www.sites.pc.gsu.edu/klanier Keisha Brown [email protected] http://sites.pc.gsu.edu/klanier 1 Why the TI-84 AND Excel? – AP Statistics College Board • “A graphing calculator is a useful computational aid, particularly in analyzing small data sets, but should not be considered equivalent to a computer in the teaching of statistics.” • “Because the computer is central to what statisticians do, it is considered essential for teaching the AP Statistics course. However, it is not yet possible for students to have access to a computer during the AP Statistics Exam.” • “The computer does more than eliminate the drudgery of hand computation and graphing — it is an essential tool for structured inquiry.” 2 Keisha Brown [email protected] http://sites.pc.gsu.edu/klanier Why the TI-84 AND Excel? – American Statistical Association’s GAISE • “We think technology should be used to analyze data, allowing students to focus on interpretation of results and testing of conditions, rather than on computational mechanics. Technology tools should also be used to help students visualize concepts and develop an understanding of abstract ideas by simulations.” • “Regardless of the tools used, it is important to view the use of technology not just as a way to compute numbers but as a way to explore conceptual ideas and enhance student learning as well. We caution against using technology merely for the sake of using technology (e.g., entering 100 numbers in a graphing calculator and calculating statistical summaries) or for pseudo-accuracy (carrying out results to multiple decimal places).” 3 Keisha Brown [email protected] http://sites.pc.gsu.edu/klanier Indeed.com Search for Graphing Calculator Keisha Brown [email protected] http://sites.pc.gsu.edu/klanier Search for Excel 8,379 4 What Other Tools Are Out There? Infographic source: http://www.predictiveanalyticstoday.com/top-statistical-software/ Keisha Brown [email protected] http://sites.pc.gsu.edu/klanier Statcrunch Tinkerplots Tableau Excel Add-Ins Tablet Apps Fathom Codap TuvoLabs NZGrapher Plotly 5 Before you begin, you need to check: Graphing Calculator • • • • What operating system do they have? 2nd, plus (MEM), 1:About TI-84 Plus CE – 5.1.5 TI-84 Plus, TI-84 Plus Silver Edition 2.55MP is the newest operating system • Is their StatWizard off or on? Keisha Brown [email protected] http://sites.pc.gsu.edu/klanier Excel • Do they have a PC or a Mac? • Which version of Excel do they have? • Do they have the Data Analysis Tool Pak installed? • File, Options, Add-Ins, Go 6 How to import/enter/share your data Graphing Calculator Excel Video Or manually type it in Keisha Brown [email protected] http://sites.pc.gsu.edu/klanier 7 Random Sampling TI-83/84 Excel 2013 • Randomly select and set a seed. • (I chose 34.) • =rand() • =randbetween(min, max) • Data Tab, Data Analysis, Random Number Generation • Select your sample. Keisha Brown [email protected] http://sites.pc.gsu.edu/klanier 8 Descriptive Statistics Mean, Sample Standard Deviation, Population standard deviation, 5 Number Summary (min, Q1, Q2, Q3, max) TI-84 Stat, CALC, 1:1-Var Stats, (Select List - OPTIONAL) Excel Type individual function names Mean = average(data) Or Data, Data Analysis, Descriptive Statistics *Make sure to select Summary Statistics* Keisha Brown [email protected] http://sites.pc.gsu.edu/klanier 9 Graphs for One Variable Histogram, Box Plot with Outliers, Box Plot Without Outliers, Dot Plot, Stem and Leaf Plot TI-84 Excel *Data, Data Analysis, Histogram* Right click on a bar for format data series N/A N/A N/A N/A N/A Insert, Column Chart Insert, Pie Chart N/A Data, Data Analysis, Regression Select Normal Probability Plot at the bottom Histogram Box Plot with Outliers Box Plot without Outliers Bar Chart Pie Chart Dot Plot, Stem and Leaf Plot, Normal Probability Plots Keisha Brown [email protected] http://sites.pc.gsu.edu/klanier 10 Bivariate Data TI-84 Excel Turn on Diagnostic, so students will see the additional menus. 2nd, 0 (Catalog), DiagnosticOn ScatterPlot r, r2, least squares regression line Keisha Brown Stat, Calc, 4:LinReg(ax+b) [email protected] http://sites.pc.gsu.edu/klanier Highlight your columns first. Insert, Scatterplot. =correl(x, y) =rsq(y, x) =slope(y, x) =intercept(y,x) OR DATA, Data Analysis, Regression 11 Probability Distributions –Discrete Excel TI-83/84 • For the new operating system, make sure the STATWIZARDS are off • Link • Stat, 1:1-Var Stats L1, L2 Keisha Brown [email protected] http://sites.pc.gsu.edu/klanier 12 Probability Distributions –Binomial TI-83/84 Excel Binompdf(n, p, x) – What is the probability of getting x successes from n trials with a probability of success p? 1.) What is the probability of getting a 100 on a 10 question multiple choice (A – D) quiz that you did not study for? Binomcdf(n, p, x) – What is the probability of getting x or less successes from n trials with a probability of success p? Keisha Brown [email protected] http://sites.pc.gsu.edu/klanier 2.) What is the probability of failing this quiz? 3.) What is the probability of scoring between a 70 and 90, inclusive? 13 Probability Distributions –Normal Excel TI-83/84 Normalcdf(lowerlimit, upper limit, mean, std. dev.) invNorm(area to the left, mean, std. dev.) Keisha Brown [email protected] http://sites.pc.gsu.edu/klanier 14 Probability Distributions –Student’s t Distribution TI-83/84 Excel To find the probability Tcdf(lower limit, upper limit, df) To find the probability =t.dist(test statistic, df, true) To find the critical values invT(α , df) To find the critical values t.inv(α, df) Keisha Brown [email protected] http://sites.pc.gsu.edu/klanier 15 Confidence Intervals (Means) TI-84 Excel Confidence Interval for a Population Mean (σ is known) Confidence Interval for a Population Mean (σ is NOT known and normal population) Confidence Interval for a Difference between means (unpaired)(𝝈𝟏 𝒂𝒏𝒅 𝝈𝟐 are known) Stat, TESTS, Z-interval *Gives the margin of error* =confidence.norm(α, σ, n) *Gives the margin of error* =confidence.t(alpha, s, n) Confidence Interval for a Difference between means (unpaired) (𝝈𝟏 = 𝝈𝟐 and are unknown) Stat, TESTS, 2-SampTInt (pool the variance) Confidence Interval for a Difference between means (unpaired) (𝝈𝟏 ≠ 𝝈𝟐 and are unknown) Stat, TESTS, 2-SampTInt (do not pool the variances) Confidence Interval for a Difference between means (paired) Put data in L1 and L2. In L3, calculate the difference. Stat, TESTS, T-interval(L3) Keisha Brown [email protected] Stat, TESTS, T-interval Stat, TESTS, 2-SampZInt http://sites.pc.gsu.edu/klanier Manual 16 Confidence Intervals (Proportions and Slope) TI-84 Excel Confidence Interval for a Population Proportion (p) Stat, TESTS, 1-PropZInt Manual Confidence interval of the difference of two independent proportions Stat, TESTS, 2-PropZInt Confidence Interval for the slope of a least-squares regression line LinRegTInt Keisha Brown [email protected] http://sites.pc.gsu.edu/klanier Data, Data Analysis, Regression *Make sure to select the Confidence Level 17 Hypothesis Testing (Means and Proportions) Hypothesis Testing For a Population Mean (σ is known) n ≥ 30 Hypothesis Testing For a Population Mean (σ is unknown) n ≤ 30 Hypothesis Testing For a 2 Independent Means (σ1 and σ2 is known) n1 and n2 ≥ 30 Hypothesis Testing with 2 Independent Means (σ1 and σ2 are unknown) TI-84 Stat, TESTS, Z-test Stat, TESTS, T-test Stat, TESTS, 2-SampZTest DATA, Data Analysis, z-Test: Two-Sample Means Stat, TESTS, 2-SampTTest =t.test(array1, array2, tails, type) If σ1 = σ2 , pooled variances = “yes” If σ1 ≠ σ2 , pooled variances = “no” Hypothesis Testing with 2 Dependent Means Excel Put data in L1 and L2. Calculate the difference in L3. Stat, TESTS, TTest(L3) Tails = 1 if a one-sided test, 2 if two-sided test Type = 2 if two-sample equal variance(homoscedastic), 3 if two-sample unequal variance (heteroscedastic) OR DATA, Data Analysis, t-Test: Two-Sample Assuming Unequal Variances OR DATA, Data Analysis, t-Test: Two-Sample Assuming Equal Variances =t.test(array1, array2, tails, type) Tails = 1 if a one-sided test, 2 if two-sided test 18 Type = 1 OR DATA, Data Analysis, t-Test: Paired Two-Sample for Means Hypothesis Testing (Proportions) TI-84 Hypothesis Testing For a Population Proportion Stat, TESTS, 1-PropZTest Hypothesis Testing with 2 Population Proportions Keisha Brown [email protected] Excel Manual Stat, TESTS, 2-PropZTest http://sites.pc.gsu.edu/klanier 19 Hypothesis Testing (Others) TI-84 Excel Chi-Square Test of Independence Stat, TESTS, 𝜒 2 − 𝑇𝑒𝑠𝑡 =chisq.test(observed, expected) Chi-Square Goodness of Fit Test *** Stat, TESTS, 𝜒 2 𝐺𝑂𝐹 − 𝑇𝑒𝑠𝑡 =chisq.test(observed, expected) L1: Observed Counts L2: Expected Counts Stat, TESTS, 2-SampFTest Data, Data Analysis, F-Test Two-Sample for Variance Hypothesis Tests for Variance *Data with the largest variance goes in list 1. ANOVA (3 or more µs) Test for the slope of a least-squares regression line Keisha Brown [email protected] Stat, TESTS, Anova( Stat, TESTS, LinRegTTest http://sites.pc.gsu.edu/klanier *Data, Data Analysis, ANOVA: Single Factor *Data, Data Analysis, ANOVA: Two-Factor with Replication *Data, Data Analysis, ANOVA: Two-Factor without Replication Data, Data Analysis, Regression Make sure to select the Confidence Level 20