Critical T Critical value for T | HP 39gs Graphing guide

Results	The results are:

	Result		Description

	Critical T		Critical value for T.
	Δ μ Min		Lower bound for μ1 – μ2.
	Δ μ Max		Upper bound for μ1 – μ2.

11-20

Inference aplet

Image 144

HP 39gs Graphing manual Critical T Critical value for T, Lower bound for μ1 μ2

Contents

Users guide Edition3 Part Number F2223AA-90001 Printing History USAEdition December June Contents Using variables in equations 10-110-6 11-1 11-411-8 11-9 13-24 Program constants 13-24 Physical constants 13-25Introduction 14-1 Storing and recalling variables 14-2 14-4 18-7 18-918-30 19-1 Service Regulatory information Preface Manual conventionsHewlett Packard’s Calculators web site can be found at Function, Polar, ParametricPage On/off, cancel operations Getting startedHome To adjust DisplayParts of the display Contrast Keyboard Menu keysInfrared or cable Aplet control keys Aplet library onDisplays the Views menu. See Aplet views on Entry/Edit keys Button performs Shifted keystrokes Helpwith Math keys Commands MenusProgram Inactive keys Reset input form values Input forms Mode settings You use the Modes input form to set the modes for Home Setting a mode Aplets E-lessons Press to return to Home Example x = cost and y = sint PolarSequence Sequence functions U in terms of n, or Another sequence, such as Un 1 Quad Explorer aplet Transformations reflected in the equation Symbolic view Plot view Press to display the aplet’s Symbolic viewAplet library Aplet views Select Plot-Table Select Plot-DetailSelect Overlay Plot Aplet view configuration Plot Setup Numeric Setup Symbolic SetupSketch view Where to start To save aplet configurationMathematical calculations Entering expressions Long results Negative numbers Scientific notation powers UsingExplicit and implicit multiplication 23 3 EEX Parentheses Entering Calculates Sin 45 + π Input Output Last input Edit line Last output Getting started Storing a value in a variable Using fractions Accessing the display history Clearing the display historySetting Fraction mode Setting fraction precision Fraction calculations SelectFraction Converting decimals to fractions Enter the calculation Evaluate the calculationFraction as Complex numbers This example, the fraction precision is set to Catalogs and editors About the Symbolic view Defining an expression Symbolic viewAplets and their views Aplet views Independent variable in the expressions is T Evaluating expressions ApletsSelect Function Home Setting up the plot Plot view setup About the Plot view Plot view settings ΘRNGΘSTEP Reset plot settings Exploring the graph Trace a graph To move between relations Zoom within a graph To jump directly to a value To turn trace on/offZoom options Square SetFactors Auto Scale Un-zoom Now un-zoom To box zoom Other views for scaling and splitting the graph Views menu options Unit. Resets default values for Split the screenMaking each pixel=1 unit. Not Pixel=π/24 radian, 7.58, or Overlay plots Decimal scalingInteger scaling Trigonometric Setting up the table Numeric view setup About the numeric view Numeric view settings Exploring the table of numbersNUM view menu keys Zoom within a table Integer Numstart and Numstep Building your own table of numbers Build a tableClear data Numtype Build Your Own Build Your Own menu keys Example plotting a circle Reset the graph setup to the default settings Function aplet, specify the functionsFunction Display the functions in numeric formPage Function aplet About the Function apletGetting started with the Function aplet Open the Function aplet Define the expressions Set up the plot Plot the functionsSpecify a grid for the graph Plot the functions Change the scale Trace a graph Select AutoScale Times Analyse graph with FCN functions Select Root Select Slope Select Signed area To find the extremum of the quadratic Select Extremum Display the numeric view Explore the tableDisplay the table of values Symbolic definition A column Display the symbolic definition for the F1 columnSymbolic definition F1 is displayed at Bottom of the screen To display Function aplet interactive analysis Select Plot FCNOr to choose a variable FCN functions RootExtremum Slope Symbolic view. Displays Shading areaIntersection Cursor. You need to have at Plotting a piecewise-defined function Parametric aplet About the Parametric apletGetting started with the Parametric aplet Define the expressions Set up the plot Plot the expression Set angle measureSet the angle measure to degrees Select Degrees Overlay plot Display the numbers Plot a triangle graph over the existing circle graph120 Page Polar aplet Getting started with the Polar apletOpen the Polar aplet Select Polar Explore the graph Display the numbers Display the Plot view menu key labels Sequence aplet About the Sequence apletGetting started with the Sequence aplet Define the expression Specify plot settings Open the Sequence apletSequence Menu keys to assist in the entry of equations Plot Setup, set the Seqplot option to Cobweb Plot the sequenceSelect Cobweb Display the . Display the table of values for this examplePage Solve aplet About the Solve aplet Getting started with the Solve aplet Open the Solve apletDefine the equation Enter known variables Select Solve Solve the unknown variable Plot the equation Modes is set to Comma, use instead Plot the equation for variable a Solve aplet’s NUM view keys areCopies the highlighted value to Displays other pages of variables, if Use an initial guess Interpreting results Plotting to find guesses Consider the equation of motion for an accelerating body To highlight T Plot the graph Press until the cursor is at the intersection Using variables in equations Linear Solver aplet Open the Linear Sequence apletSelect Linear Solver Solver was able to find solutions for x, y, and z as Hence we need the three-equation input form Linear Solver aplet Page Triangle Solve aplet About the Triangle Solver aplet Open the Triangle Solver aplet Triangle Solver Errors Not enough data Addition, you cannot specify only angles and no lengths Statistics aplet About the Statistics apletGetting started with the Statistics aplet Enter data Select StatisticsEnter the data into the columns To move to the next column Select a fit in the Symbolic setup view Choose fit and data columns Explore statisticsValue is Setup plot Plot the graph Draw the regression curve Display the equation for best linear fitTo move to the FIT1 field Slope m is 425.875. The y-intercept b is Predict values To highlightStat-Two Entering and editing statistical data Statistics aplet’s Numeric view keys are Statistics Expression in standard Mathematical form. Press When Done Copies the column variable orVariable expression to the edit line Expression Clear is used Data sets will need to be selectedAgain before re-use Save data Edit a data set Plot a histogram of the data Delete data Insert data Sort data values Angle Setting Defining a regression modelTo choose the fit Fit models To define your own fit Computed statistics 7,8,15,16,17 Plotting Two-variableColumns for a linear fit only Plot types Histogram Box and Whisker PlotTo plot statistical data Fitting a curve to 2VAR data Scatter PlotCorrelation coefficient Setting up the plot Plot setup view Relative ErrorPlotting mark 2VAR Connected points 2VAR Trouble-shooting a plot Statistics aplet’s Plot view keysErases the plot Calculating predicted values Find predicted valuesAccording to the current regression Model Statistics aplet 10-21 Page Inference aplet About the Inference apletGetting started with the Inference aplet Open the Inference aplet Table below summarizes the options available Symbolic view Inference aplet’s Symb view keys Setup-NUM Select the inferential method Enter dataSelect Hypoth Test Test 1 μ Are explained in the feature of this aplet Importing sample statistics from the Statistics aplet If the Decimal Mark setting in the Modes input form Statistics aplet opens in the Numeric viewC1 column, enter the random numbers Produced by the calculator 529 295 952 259 925 592 Set up the interval calculation Open Inference apletInference Select Conf Interval Display Numeric view Display Plot view Specify a 90% Confidence interval in the C fieldTo move to the C field Hypothesis tests One-Sample Z-TestMenu name Inputs Two-Sample Z-Test Results One-Proportion Z-Test Population 2 standardTest 1π Measures the strength of the evidence for a selected Two-Proportion Z-Test One-Sample T-Test Sample standard deviation With the α level that you Two-Sample T-Test Pooled? Confidence intervals One-Sample Z-Interval Two-Sample Z-Interval One-Proportion Z-Interval Two-Proportion Z-Interval One-Sample T-Interval Two-Sample T-Interval Pooled Critical T Critical value for T Using the Finance Solver Background 3 4 Compounding period -- which is Performing TVM calculations PMT Example 1 Loan calculations Example 2 Mortgage with balloon payment Calculating Amortizations To calculate amortizationsExample 3 Amortization for home mortgage To continue amortizing the loan Example 4 Amortization for home mortgage Using mathematical functions Math functionsMath menu Name. Note You do not need to press first Math functions by category Function categoriesSyntax Functions common to keyboard and menus Keyboard functions Value1+ value2 , etcEvalue E5 returns Returns LOG100 returns ABS1,2 returns Calculus functions Nthroot 8 returns∂ s1s1 2+3*s1 returns 2*s1+3 S1,2*X+3,X Complex number functions TaylorARG Conj Constants ConversionsMaxreal Minreal Hyperbolic trigonometry List functions Loop functions Matrix functions Polynomial functionsPolycoef Polyeval Probability functions PolyrootComb Perm Real-number functions DEG→RAD FloorFnroot Frac INT MantMAX MIN Total RAD→DEGRound Sign Symbolic functions Two-variable statisticsXpon Isolate Test functions QuadQuote QUADX-12-7,X returns Trigonometry functions IfteNot XOR Symbolic calculations Finding derivatives To find derivatives in Home To find derivatives in the Function aplet’s Symbolic view Evaluate the function Show the resultSelect F2X and evaluate it To find the indefinite integral using formal variables You could also just defineFor example, to find the indefinite integral Program constants and physical constants Program constants Physical constants 13-26 Variables and memory management Introduction Storing and recalling variables To use variables CalculationsTo clear a variable Vars menu Open the Vars menuPress Add the contents of two list variables, and to store Names or values of variables into programsExample Result in another list variable 14-6 That you can configure using To store into a graphics variable on17-5 for more information on To access an aplet X0, Y0 to X9, Y9 Symbolic view. SeeVariable Aplet variables on page R-7 Memory Manager Line, press and pressDetails of variables within the category To delete variables in a categoryPage Matrices VectorsMatrices Matrix Variables Creating and storing matrices Matrix Catalog keysPOLYROOT1,0,-1,0 M1 To create a matrix in the Matrix Catalog Working with matrices To transmit a matrix Deletes the highlighted cells, row Or column you are prompted toMake a choice Moves to the first row, last row, first Matrix arithmetic To store one elementCreate the second matrix Matrices 15-7 Solving systems of linear equations Open the Matrix catalog and create a vector Select Real matrix Matrix functions and commands About commandsArgument conventions About functions Cond CrossDET DOT Makemat RankRownorm Rref Examples Transposing a Matrix Reduced-Row Echelon Form Matrices 15-15 Page Lists You can create, edit, delete, send, and receive named List catalog keys Create a list List edit keys Displaying and editing lists To display a listTo display one Element A list To insert an element 1. Open the List catalogPress , and press 148 L12 List functions Deleting listsTransmitting lists To delete a list 2,3 returns 5,10,15 CONCATlist1,list2CONCAT1,2,3,4 returns 1,2,3,4 ΔLISTlist1 23 27 Calculates the product of all elements in list ΠLISTlistΠLIST2,3,4 returns Finding statistical values for list elements 16-10 Aplet note view To write a note in Note viewYour work is automatically saved. Press any view key Or to exit the Notes view Contents of variables CommandsSpace key for text entry Alpha-lock for letter entry Aplet sketch view Sketch keysTo draw a line To draw a box Draw keys Press to continue drawing, or press Mynote Opens the selected note for Begins a new note, and asksFor a name Another HP 39gs or PC Press instead Contents of a Program Structured Programming Programming Program catalog Open Program CatalogBe simple-or it can be divided further into other Programs that perform smaller tasks Program catalog keys Creating and editing programs Create a new programPress Progrm to open the Program catalog On the left, use or to highlight a command Press to paste the command into the program editorEdit a program 1. Press Progrm to Editing keys Using programs Run a program Debug a program Stop a program Transmit a program Customizing an aplet Aplet naming convention Example Configuring the Setviews menu option programs Save the aplet Setviews ’’’’ ’’’’18 ’’My Entry1’’’’EXP.ME1’’1’’My Entry2’’’’EXP.ME2’’3 ’’ ’’’’EXP.SV’’0 Programming commands ’’’’’’EXP.ANG’’0’’Start’’’’EXP.S’’7 Aplet commands CheckSelect Setviews Associating programs with your aplet Auto-run programs ProgramName ViewNumberIncluding standard menu options Branch commands UncheckIF...THEN...END Uncheck n IF... THEN... Else END CASE...END Iferr Then ELSE…END If A==1 Drawing commands RUNStop BOX EraseFreeze Line Graphic commands Grobxor MakegrobPLOT→ →PLOT Loop commands Matrix commands Randmat RedimScale Scaleadd Print commands Prompt commands Clrvar DispDispxy Disp 3A is 2+2 Disptime 51.52HELLOEditmat matrixname Getkey InputMsgbox Stat-One and Stat-Two commands Stat-One commandsStat-Two commands Storing and retrieving variables in programs Plot-view variables Grid Hmin/HmaxIndep InvCross Isect LabelsRecenter Root S1mark-S5mark SeqPlotSimult Slope Umin/Umax UstepTmin / Tmax Tracing Tstep XcrossYcross Ytick Ymin / Ymax Yzoom Symbolic-view variables S1fit...S5fit Cubic S2fit Numeric-view variables C1...C9, C0Digits Format NumCol NumFontNumIndep NumRow NumStep NumTypeNumZoom StatMode Sketch variables PageNumFollowing aplet variable is available in Note view Graphicname Extending aplets Creating new aplets based on existing aplets Open the Solve aplet and save it under the new name SolveDegrees Resetting an aplet Using a customized apletChoose the sine formula in E1 Downloading e-lessons from the web Sending and receiving apletsHewlett-Packard’s Calculators web site can be found at To transmit an aplet Sorting items in the aplet library menu list To sort the aplet list To delete an aplet Reference information GlossaryExpression line# Cross matrix1,matrix2 Editor and catalog Matrix Two-dimensional array of values Record using the Program editorVector One-dimensional array of values Set to Comma and enclosed Resetting the HP 39gs To erase all memory and reset defaultsTo reset using the keyboard Operating details If the calculator does not turn onBatteries To install the main batteries To install the backup battery Variables Home variables Function aplet variables Area Root Extremum Slope IsectAngle Parametric aplet variables Parametric aplet variables are Category Available name Plot Polar aplet variables Polar aplet variables are Category Available names Plot Sequence aplet variables Sequence aplet variables are Category Available name Plot Solve aplet variables Solve aplet variables are Category Available name PlotDigits NumCol Format NumRow Statistics aplet variables Math menu categories Math functionsMath functions are Category Available name Calculus Hyperb Category Available name Matrix Polynom Degrees Grads Radians Standard Sci Fixed Eng FractionCobweb Stairstep Stat1Var Stat2Var Compt w... Compton Wavelength, λc Program commands Program commands are Category Command ApletBranch Print Category Command Stat-Two Status messages Also be correct. Look up Function name in the index toFind its proper syntax Function value, root, extremumPage Limited Warranty HP 39gs Graphing Calculator Warranty period 12 monthsPage Service Canada 905 206-4663 or Rotc = Rest of the country Regulatory information Xxxx This marking is valid for EUPage Page Index Branch structures 18-17 build your own table Contrast Freeze 18-20 Line 18-20 Pixoff 18-20 Pixon 18-20 Tline Grobor Acosh Alog Asinh Atanh Cosh EXPPage Page Angle measure 1-10 decimal mark 1-11 number format Trigonometric scaling 2-14 two-variablestatistics Sending and receiving 18-8 structured Menu lists 1-8 speed searches Navigate around 3-8 numeric values 3-7 numeric view setup Page