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Casio FX-9750G, FX-9860GII S1-Prop Z Test, S2-Sample Z Test

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• [Save Res] does not save the Μ condition in line 2.

S2-Sample Z Test

This test is used when the standard deviations for two populations are known to test the hypothesis. The 2-SampleZ Test is applied to the normal distribution.

Perform the following key operations from the statistical data list.

(TEST)

(Z)

(2-S)

The following shows the parameter data specification items that are different from list data specification.

Calculation Result Output Example

Μ1ξΜ2 ............	direction of test
sx1 ................	Displayed only for Data: List setting.
sx2 ................	Displayed only for Data: List setting.

• [Save Res] does not save the Μ1 condition in line 2.

S1-Prop Z Test

This test is used to test for an unknown proportion of successes. The 1-PropZ Test is applied to the normal distribution.

Perform the following key operations from the statistical data list.

(TEST)

(Z)

(1-P)

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Contents

CASIO Worldwide Education Website CASIO EDUCATIONAL FORUM Page Getting Acquainted — Read This First Chapter 1 Basic Operation Chapter 2 Manual Calculations Chapter 3 List Function Chapter 4 Equation Calculations Chapter 6 Statistical Graphs and Calculations Chapter 7 Financial Calculation (TVM) Chapter 8 Programming Chapter 9 Spreadsheet Chapter 10 eActivity Chapter 12 System Manager Chapter 13 Data Communications Chapter 14 Using SD Cards (fx-9860GⅡ SD only) Appendix E-CON2Application Getting Acquainted — Read This First IAbout this User’s Guide IContrast Adjustment Basic Operation IKey Table IKey Markings ISelecting Icons The following explains the meaning of each icon Icon Mode Name S • SHT STAT mode IAbout the Function Menu IAbout Display Screens INormal Display ISpecial Display Formats IInputting Calculations IEditing Calculations IUsing Replay Memory IMaking Corrections in the Original Calculation IUsing the Clipboard for Copy and Paste kCatalog Function Example To use the Catalog to input the ClrGraph command 4. Using the Math Input/Output Mode RUN • MAT kInput Operations in the Math Input/Output Mode SUsing the MATH Menu log b f(x)dx } SMath Input/Output Mode Input Examples To input 23 + To input 1+ x + 1dx To input 2 ⋅ SWhen the calculation does not fit within the display window SMath Input/Output Mode Input Restrictions SUsing Values and Expressions as Arguments Original Expression After Expression SEditing Calculations in the Math Input/Output Mode IUsing Undoing and Redoing Operations IMath Input/Output Mode Calculation Result Display IHistory Function IUsing the Clipboard for Copy and Paste in the Math Input/Output Mode ICalculation Operations in the Math Input/Output Mode IPerforming Matrix Calculations Using Math Input/Output Mode IUsing Graph Modes and the EQUA Mode in the Math Input/Output Mode and then uMath Input/Output Mode Input in the GRAPH Mode Make sure that initial default settings are configured on the View Window Example 2 In the GRAPH mode, input the function y=∫x graph it • Math Input/Output Mode Input and Result Display in the EQUA Mode 5. Option (OPTN) Menu RUN CPLX CONV HYP 6. Variable Data (VARS) Menu {V-WIN}/{FACT}/{STAT}/{GRPH}/{DYNA}/{TABL}/{RECR}/{EQUA}/{TVM}/{Str} SV-WIN— Recalling V-Windowvalues R-X R-Y INPT •{RESLT}* ... {statistical calculation output values} RESLT •{TEST} ... {test calculation results} Chi 7.Program (PRGM) Menu COM CTL CLR ISetup Screen Function Key Menus SMode (calculation/binary, octal, decimal, hexadecimal mode) Comp Dec Hex Oct SList File (list file display settings) FILE SSub Name (list naming) SGraph Func (function display during graph drawing and trace) SDual Screen (dual screen mode status) 9. Using Screen Capture u To capture a screen image IGetting the Calculator Back to its Original Mode Settings kRestart and Reset kLow Battery Message Chapter 2 Manual Calculations IArithmetic Calculations INumber of Decimal Places, Number of Significant Digits, Normal Display Range ICalculation Priority Sequence ICalculation Result Irrational Number Display SCalculation Result Display Range with a'b d'e a´'b + d´'e Calculation Examples IMultiplication Operations without a Multiplication Sign IOverflow and Errors IMemory Capacity ICalculations Using Variables IMemory Example 2 To add 456 to variable A and store the result in variable B SString Memory To assign string “ABC” to Str 1 and then output Str 1 to the display SFunction Memory STO RCL STo store a function To store the function (A+B) (A–B)as function memory number STo recall a function To recall the contents of function memory number STo recall a function as a variable kAnswer Function IPerforming Continuous Calculations ISetting the Angle Unit ISetting the Display Format IFunction Menus SHyperbolic Calculations (HYP) sinh cosh tanh SProbability/Distribution Calculations (PROB) IAngle Units ITrigonometric and Inverse Trigonometric Functions ILogarithmic and Exponential Functions IHyperbolic and Inverse Hyperbolic Functions IOther Functions IRandom Number Generation (RAND) RanList# Examples SRandom Integer Generation (RanInt#) 1 10 5U SRandom Number Generation in Accordance with Normal Distribution (RanNorm#) ICoordinate Conversion IPermutation and Combination IGreatest Common Divisor (GCD), Least Common Multiple (LCM) IDivision Remainder (MOD), Remainder of Exponential Division (MOD Exp) IFractions IEngineering Notation Calculations ILogical Operators (AND, OR, NOT, XOR) IQuotient of Integer ÷ Integer IRemainder of Integer ÷ Integer ISimplification ISolve Calculations ISolving an f(x) Function IDifferential Calculations IQuadratic Differential Calculations IIntegration Calculations f(x), a, b, tol) abf(x)dx f(x)dx +.....+ b f(x)dx I3 Calculations IMaximum/Minimum Value Calculations 6. Complex Number Calculations Arg Conj ReP ImP IArithmetic Operations IReciprocals, Square Roots, and Squares IComplex Number Format Using Polar Form IAbsolute Value and Argument IConjugate Complex Numbers a– bi IExtraction of Real and Imaginary Parts IPolar and Rectangular Form Transformation [OPTN]-[CPLX]-[rƧ]/[a+bi] 7.Binary, Octal, Decimal, and Hexadecimal Calculations with Integers ISelecting a Number System INegative Values and Bitwise Operations INumber System Transformation STo convert a displayed value from one number system to another To convert 2210 (default number system) to its binary or octal value 8. Matrix Calculations About Matrix Answer Memory (MatAns) IInputting and Editing Matrices IMatrix Cell Operations SRow Calculations Swap Rw+ STo swap two rows To swap rows two and three of the following matrix: SRow Operations STo delete a row STo insert a row To insert a new row between rows one and two STo add a row IModifying Matrices Using Matrix Commands Example To input the following data as Matrix A: STo input an identity matrix To create a 3 σ 3 identity matrix as Matrix A STo check the dimensions of a matrix SModifying Matrices Using Matrix Commands STo assign values to and recall values from an existing matrix [OPTN]-[MAT]-[Mat] Example 1 To assign 10 to the cell at row 1, column 2 of the following matrix: Matrix A = 3 STo fill a matrix with identical values and to combine two matrices into a IMatrix Calculations SMatrix Arithmetic Operations Example 1 To add the following two matrices (Matrix A + Matrix B): Example 2 To multiply the two matrices in Example 1 (Matrix A σ Matrix B) SDeterminant Obtain the determinant for the following matrix: SRow Echelon Form To find the row echelon form of the following matrix: SReduced Row Echelon Form To find the reduced row echelon form of the following matrix: −21 SSquaring a Matrix [x2] To square the following matrix: SRaising a Matrix to a Power To raise the following matrix to the third power: 9.Metric Conversion Calculations IPerforming a Unit Conversion Calculation IUnit Conversion Command List Page Chapter 3 List Function IEditing List Values INaming a List ISorting List Values IAccessing the List Data Manipulation Function Menu To transfer the contents of List 1 (2, 3, 6, 5, 4) to column 1, and the contents of List 2 (11, 12, 13, 14, 15) to column 2 of Matrix Answer Memory STo count the number of data items in a list [OPTN]-[LIST]-[Dim] To count the number of values in List 1 (36, 16, 58, 46, 56) STo create a list by specifying the number of data items To create five data items (each of which contains 0) in List STo generate a sequence of numbers[OPTN]-[LIST]-[Seq] To input the number sequence 12, 62, 112, into a list, using the function f(x) = X2. Use a starting value of 1, an ending value of 11, and an increment of STo find the minimum value in a list STo calculate the median of data items of specified frequency [OPTN]-[LIST]-[Med] To calculate the median of values in List 1 (36, 16, 58, 46, 56), whose frequency is indicated by List 2 (75, 89, 98, 72, 67) STo combine lists STo calculate the cumulative frequency of each data item [OPTN]-[LIST]-[Cuml] STo calculate the percentage represented by each data item [OPTN]-[LIST]-[%] To calculate the percentage represented by each data item in List (2, 3, 6, 5, 4) STo calculate the differences between neighboring data inside a list IError Messages IInputting a List into a Calculation IRecalling List Contents IGraphing a Function Using a List IInputting Scientific Calculations into a List IPerforming Scientific Function Calculations Using a List Chapter 4 Equation Calculations 2.High-orderEquations from 2nd to 6th Degree a μ b μ c μ … To solve the cubic equation (Angle unit = Rad) x3 – 2x2 – x + 2 3. Solve Calculations An object thrown into the air at initial velocity V takes time T to reach height H. Use the following formula to solve for initial velocity V when H = 14 (meters), T = 2 (seconds) and gravitational acceleration is G 9.8 (m/s2) Graphing IHow to draw a simple graph (1) IHow to draw a simple graph (2) IV-Window(View Window) Settings STo make V-Windowsettings Rectangular coordinate parameter Polar coordinate parameter INIT TRIG IV-WindowMemory ISpecifying the Graph Range IZoom ISpecifying the Graph Type IStoring Graph Functions STo store a parametric function To store the following expressions in memory areas Xt3 and Yt3: x = 3 sinT y = 3 cosT STo create a composite function IEditing and Deleting Functions ISelecting Functions for Graphing IGraph Memory ICopying the Graph to the Sub-screen IRectangular Coordinate Graph IDrawing Multiple Graphs on the Same Screen IUsing Copy and Paste to Graph a Function IStoring a Function and Generating a Number Table STo generate a table using a table range To generate a table as the value of variable x changes from –3to 3, in increments of STo generate a table using a list SGenerating a Table To generate a table of values for the functions stored in memory areas Y1 and Y3 of the Table relation list IEditing Tables ICopying a Table Column to a List IDrawing a Graph from a Number Table ISimultaneously Displaying a Number Table and Graph IUsing Dynamic Graph IDrawing a Dynamic Graph Locus IGraph Calculation DOT Switching Function IUsing Dynamic Graph Memory IGenerating a Number Table from a Recursion Formula IGraphing a Recursion Formula IGraphing a Phase Plot from Two Numeric Sequences Page IWEB Graph (Convergence, Divergence) IGraphing a Conic Section IDrawing a Line Draw a line that is tangent to point (2, 0) on the graph for y = x (x + 2) (x – 2) IReading Coordinates on a Graph Line IDisplaying the Derivative IGraph to Table ICoordinate Rounding ICalculating the Root ICalculating the Point of Intersection of Two Graphs IDetermining the Coordinates for Given Points ICalculating the lntegral Value for a Given Range IConic Section Graph Analysis STo calculate the focus and length of latus rectum [G-SLV]-[FOCS]/[LEN] To determine the focus and length of latus rectum for the parabola X (Y – 2)2 + Xmin = –1 Statistical Graphs and Calculations IChanging Graph Parameters 1. General graph settings • Frequency • Mark Type STo display the general graph settings screen •StatGraph (statistical graph specification) •Graph Type (graph type specification) Scat NPP 2. Graph draw/non-drawstatus INormal Probability Plot IPie Graph IHistogram IMed-boxGraph IBar Graph INormal Distribution Curve IBroken Line Graph IDisplaying the Calculation Results of a Drawn Single-VariableGraph ICalculation Methods for the Std and OnData Settings Median SOnData 4/10 8/10 IDrawing a Scatter Diagram and xy Line Graph IDrawing a Regression Graph ISelecting the Regression Type IDisplaying Regression Calculation Results IGraphing Statistical Calculation Results ILinear Regression Graph IMed-MedGraph IQuadratic/Cubic/Quartic Regression Graph ILogarithmic Regression Graph IExponential Regression Graph IPower Regression Graph ISinusoidal Regression Graph ILogistic Regression Graph 1 + ae–bx IResidual Calculation IDisplaying the Calculation Results of a Drawn Paired-VariableGraph ICopying a Regression Graph Formula to the GRAPH Mode ISingle-VariableStatistical Calculations IPaired-VariableStatistical Calculations IRegression Calculation (yi – (axi + b))2 (yi – (a + bxi))2 (yi – (axi 2 + bxi + c))2 (yi – (axi3+ bxi2+ cxi + d ))2 (yi – (axi4+ bxi3 + cxi2 + dxi + e))2 IEstimated Value Calculation (, ) INormal Probability Distribution Calculation IDrawing a Normal Probability Distribution Graph ICalculations Using the Distribution Function IDetermining Standard Deviation and Variance from List Data ICalculations Using the TEST Command 1-Sample 2-Sample 1-Prop 2-Prop LinearReg IZTests S2-Sample Z Test S1-Prop Z Test ItTests S 1-Sample t Test S2-Sample t Test SLinearReg t Test IƵ2 Test I2-Sample F Test IANOVA Page IANOVA (Two-Way) SInput Example SResults 6. Confidence Interval Interval SGeneral Confidence Interval Precaution IZ Interval It Interval S2-Sample t Interval 7. Distribution Normal probability density Normal cumulative distribution Inverse normal cumulative distribution Student ICommon Distribution Functions INormal Distribution • Normal Cumulative Distribution • Inverse Normal Cumulative Distribution f (x)dx = p IStudent-t Distribution IƵ2 Distribution IF Distribution IBinomial Distribution • Binomial Cumulative Distribution • Inverse Binomial Cumulative Distribution IPoisson Distribution IGeometric Distribution • Geometric Cumulative Distribution • Inverse Geometric Cumulative Distribution (DIST)(E)(GEO)(InvG) IHypergeometric Distribution Interval, and Distribution (All models except fx-7400GII) IInput Terms Page IOutput Terms ITest IConfidence Interval IDistribution (Continuous) IDistribution (Discrete) Chapter 7 Financial Calculation (TVM) ISetup Items IGraphing in the TVM Mode SFV REPT 3. Compound Interest SPV, PMT, FV, n 39 )9 SI % PV + Α σ 307 + σ FV P/Y C/Y Inputting Values 4. Cash Flow (Investment Appraisal) NPV NFV IRR PBP NPV = CF0 + NFV = NPV σσ(1 + i )n 0 = CF0 + CF1 CF2 5. Amortization ,17 BAL sign 6. Interest Rate Conversion EFF EFF APR σσn σ100 SEL 05*(%) = 1– &67SEL σ 8.Day/Date Calculations d1+D d1–D •360-dayDate Mode Calculations 9. Depreciation SYD SStraight-LineMethod (SL) SL1 (PV–FV ) {Y–1} SDeclining-BalanceMethod (DB) I% Y–1 DB1 = PV σ 100n σ RDV1 = PV – FV – DB1 I% DBj = (RDVj–1 + FV ) σ 100n YLD/100 Page PRD 11. Financial Calculations Using Functions To calculate the total interest and principal paid for a 2-year (730-day) $300 loan at a simple annual interest rate of 5%. Use a Date Mode setting of Chapter 8 Programming 2.PRGM Mode Function Keys NEW SWhen you are registering a file name BASE SYBL IDebugging a Program ISearching for Data Inside a Program ISearching for a File IEditing a File Name IDeleting a Program IRegistering a password IRecalling a Password Protected Program ICommand Index IBasic Operation Commands IProgram Commands (COM) IProgram Control Commands (CTL) Example: Return Syntax: Return Syntax: Stop IJump Commands (JUMP) (Jump Code) Menu Example: Lbl 2 IClear Commands (CLR) IDisplay Commands (DISP) DrawFTG-Con, DrawFTG-Plt DrawGraph DrawR-Con, DrawR-Plt DrawR3-Con, DrawR3-Plt DrawStat IInput/Output Commands (I/O) Locate Example: Cls Receive( / Send OpenComport38k / CloseComport38k IConditional Jump Relational Operators (REL) IStrings Exp ExpStr StrCmp Strlnv StrJoin StrMid StrRight StrRotate StrShift StrSrc IOther IText Display IUsing Matrix Row Operations in a Program (Not available on the fx-7400GII) IUsing Graph Functions in a Program IUsing Dynamic Graph Functions in a Program IUsing Table & Graph Functions in a Program IUsing Recursion Table & Graph Functions in a Program IUsing List Sort Functions in a Program IUsing Statistical Calculations and Graphs in a Program IUsing Distribution Graphs in a Program •To draw a Student-t cumulative distribution graph •To draw a Ƶ2 cumulative distribution graph •To draw an F cumulative distribution graph IPerforming Statistical Calculations in a Program IPerforming Distribution Calculations in a Program • Student-t Distribution tPD(: tCD(: InvTCD(: •Ƶ2 Distribution •Binomial Distribution BinomialPD(: BinomialCD(: InvBinomialCD(: •Poisson Distribution IUsing the TEST Command to Execute a Command in a Program TwoSample OneProp TwoProp • t Test OneSampleTTest: TwoSampleTTest: Syntax : LinRegTTest: Bdf IPerforming Financial Calculations in a Program Cmpd_FV: Cash_IRR: Cash_PBP: Cash_NFV: •Amortization 7. PRGM Mode Command List RUN Program (MENU) key Command *key )key )(PRGM) key K(SET UP) key key BASE Program Program Name Prime Factorization Ellipse Chapter 9 Spreadsheet ISpreadsheet Screen Function Menu ISpreadsheet File Operations IRecalculating All of the Formulas in the Currently Open Spreadsheet IUsing the Cell Cursor IData (Constants, Text, Formula) Input Basics IInputting a Constant (Value, Calculation Result, Number Sequence) into a Cell IInputting Text into a Cell IInputting a Formula into a Cell IInputting a Cell Reference Name IRelative and Absolute Cell Reference Names ICopying and Pasting Cell Contents ICutting and Pasting Cell Contents IInputting the Same Formula into a Range of Cells ISorting Constant Data IDeleting and Inserting Cells STo delete the contents of all the cells in a spreadsheet STo insert a row or column of blank cells •To insert rows •To insert columns STo clear the contents of specific cells ISpecial S • SHT Mode Command List IS • SHT Mode Command Example IExample of Statistical Graph Operations (GRPH Menu) IGeneral Graph Settings Screen Operations IExample of Statistical Calculation Operation (CALC Menu) IUsing the Statistical Calculation Data Range Specification Screen ISTAT Mode and S • SHT Mode Function Menu Correspondence Table ISaving Spreadsheet Data to a Memory IRecalling Data from Memory to a Spreadsheet eActivity IFile List Function Menu IWorkspace Screen Function Menu TEXT STOP •Menu when a Text Line is Selected 3.eActivity File Operations ICursor Movement and Scroll Operations IInputting into a Text Line IInputting into a Calculation Line IInserting a Calculation Stop Line IUsing Strips Strip Data Type Table Data Type Strip Name STo insert a strip Page SNotes Strips STo change the title of a strip STo call an application from a strip kSaving a File kDisplaying the eActivity Memory Usage Screen Page Chapter 11 Memory Manager IMemory Information Screen Main Memory Data Name Contents ICreating a Folder in Storage Memory or on an SD Card ISelecting Data ICopying Data IError Checks During Data Copy IDeleting Files IBacking Up Main Memory Data STo restore backup data to the main memory IOptimizing the Storage Memory or SD Card Memory Chapter 12 System Manager IPower Properties Settings ISystem Language Setting IVersion List IReset Function Key Functions Chapter 13 Data Communications II kSelect Connection Mode Screen (All models except fx-7400GII) IPerforming a Data Transfer Operation IConfiguring the Receiver’s Wakeup Feature 4.Data Communications Precautions Data Item Overwrite Check*1 Page kExchanging Data with another Model Calculator S • SHT u Sending Data from an OS 2.0 Calculator to any Older Model Calculator Invalid Data Size Complex Number in data Invalid Data Number u Sending Data from an OS 2.0 Calculator to a CFX-9850GSeries Calculator u Sending Data from an OS 2.0 Calculator to an fx-7400GSeries Calculator Page u Sending Data from an fx-9860GSeries Calculator to an OS 2.0 Calculator u Sending Data from a CFX-9850GSeries Calculator to an OS Calculator 5. Screen Image Send ISelect Connection Mode Screen (All models except fx-7400GII) ITransferring Screen Images to a Computer IAuto Screen Image Send to an OHP Unit (Not available on the fx-7400GII) IAuto Screen Image Send to a Computer Using the fx-9860GManager PLUS Connecting to a Projector STo project calculator screen contents from a projector SPrecautions when Connecting Chapter 14 Using SD Cards Important STo insert an SD card STo remove the SD card IRecommended SD Card Types Appendix Page Page Page nCr ab/c Input range Page Page 1E-CON2Overview Note About online help kSetup Wizard Parameters uTo configure an EA-200setup using Setup Wizard Before getting started Important If you select this sensor/option: Go here for more information: Page kUsing Setup Wizard to Configure Settings for FFT (Frequency Characteristics) Data Sampling kUsing Setup Wizard to Configure a PhotoGate Setup u To configure a setup for PhotoGate and Smart Pulley kOutputting the Waveform of a Function through the Speaker Page To change the output frequency and try again: To change the output range of the waveform graph and try again: To change the function: To exit the procedure and return to the E-CON2main menu: kAdvanced Setup Operations uTo return setup parameters to their initial defaults kChannel Setup Page kSample Setup Page u To configure the Distance setting u To configure the FFT Graph setting kTrigger Setup u To configure Trigger Setup settings u To specify the countdown start time u To specify microphone sensitivity u To specify the trigger threshold value and trigger edge type u To configure PhotoGate trigger start and end settings u To specify the trigger threshold value and motion sensor level kGraph Setup Page kConfiguring a Custom Probe Setup Page kAuto Calibrating a Custom Probe Page kZero Adjusting a Custom Probe kManaging Custom Probe Setups 5 Using the MULTIMETER Mode u To use the MULTIMETER Mode kSaving a Setup kUsing and Managing Setups in Setup Memory uTo recall a setup and use it for sampling uTo change the name of setup data uTo delete setup data uTo recall setup data kConverting a Setup to a Program Page Page kConverting a CFX-9850Series Program to a fx-9860Series Compatible Program Page kBefore getting started kStarting a Sampling Operation uTo start sampling uOperations during a sampling operation Starts Sampling kManaging Sample Data Files Page u To rename an existing sample data file u To delete a sample data file kAccessing Graph Analysis Tools kSelecting an Analysis Mode and Drawing a Graph Page u To deselect sampled data assigned for graphing on the Graph Mode screen kGraph Screen Key Operations kScrolling the Graph Screen kUsing Trace kUsing Zoom kTransforming Sampled Data to List Data kUsing Fourier Series Expansion to Transform a Waveform to a Function Page kPerforming Regression kOverlaying a Y=f(x) Graph on a Sampled Result Graph kWorking with Multiple Graphs Page kOutputting a Specific Range of a Graph from the Speaker Page kConfiguring View Window Parameters 12 Calling E-CON2Functions from an eActivity uEcon SetupWizard strip uEcon AdvancedSetup strip uEcon Sampling strip uEcon Graph strip kInserting an Econ Strip into an eActivity File kCalling an E-CON2Function from an Econ Strip u To access Advanced Setup from an Econ Advanced Setup strip u To execute sampling from an Econ Sampling strip u To graph sampled data from an Econ Graph strip u Econ Strip Memory Capacity Precautions This mark applies in EU countries only