User manual HP 40G

[. . . ] hp 39g+ graphing calculator Mastering the hp 39g+ A guide for teachers, students and other users of the hp 39g+, hp 39g & hp 40g Edition 1. 1 HP part number F2224-90010 Printed Date: 2005/10/11 Table of Contents Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 How to use this Manual. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 Early High School. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 Pre-Calculus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . [. . . ] . Change to the SYMB view, move the highlight to the equation of the regression line and press . places, this gives an equation of N = 13 8950 e06579t . (ii) Predict N for t = 15 hours. Change to the HOME view and use the PREDY function or use the facilities in the PLOT view. (iii) Find t so that N = 2 N 0 . The value of N 0 is the y intercept of the line of best fit. These values from the curve of best fit are not directly accessible but can be retrieved using the PREDY function (see page 145). This is shown in the screen shown right. Store the results into memories A and K. This saves having to re-type them from the screen. Now switch to the Solve aplet and enter the equation to be solved. Changing into the NUM view, you should find the values of A and K already defined (that was why we stored the curve values into the appropriate memories), so move the highlight to T and press . Result: Doubling time is 1. 0536 hours. 149 THE INFERENCE APLET This aplet is a very flexible tool for users investigating inference problems. It provides critical values for hypothesis testing and confidence intervals, and does this not only quickly but in a visually helpful format. Before we look at the Inference aplet in detail I am going to take a small digression to look at a simple inferential problem which can be solved using only the Statistics and Solve aplets. Using the Chi2 test on a frequency table "Four coins are tossed 400 times and the number of heads noted for each toss. Using the Chi2 test at a 5% level of confidence, indicate whether the coins may be biased. " Number of heads Frequency 0 32 1 112 2 158 3 90 4 8 We would expect that for an un-biased set of coins the distribution would be binomial. Our hypotheses are: H0: The number of heads is binomially distributed (n=4 & p=0. 5) HA: The number of heads is not binomially distributed (n=4 & p=0. 5) Begin by entering the data into the first two columns of the Statistics aplet (right). We now need to calculate the expected values based on our null hypothesis. We can do this in the HOME view using the calculation shown right (and below), inserting the results into column C3. 400*COMB(4, C1)*. 5^C1*. 5^(4-C1) C3 We can now calculate the X2 value using the calculations shown right, which places the individual values into column C4 for inspection if required. 150 The values can be seen by changing to the NUM view. In the MATH menu, Probability section, there is a function called UTPC (Upper-Tailed Probability Chi-squared) which will give the critical X2 probability for a supplied number of degrees of freedom and a value. In this case we would like the value for a given probability so we will enter the formula into the Solve aplet. Change to the NUM view, enter the known for parameters of D=4 and P=0. 05, and 2 the critical X value. Since our value of 16. 387 is larger than the critical value of 9. 488 we conclude that we must reject the null hypothesis and judge that the observed values do not follow this binomial distribution and hence that the coin is probably biased. This does not say that it is not binomially distributed; just not with those parameters. [. . . ] Using them you can choose: · · · · · · · · Quit config (when you're finished making changes) Complex (or Real) Approx (or Exact) Direct (or Step by Step see following page) 1 + x + x² (or x² + x +1 ; governs how polynomials will display) Sloppy (or Rigorous, if you want to work in absolute values) Num. factor (or Symb factor) Cmplx vars (or Real vars if you want all symbolic variables to be assumed to be and treated as real) · English (or Français if you want the help screens to be in French) · Default cfg (which is R = STEP X 13 ||). 329 Pressing takes you out of the CFG menu (as does choosing QUIT from the menu and confirming it with ) but does not discard any changes you have made. The name of the current variable, as well as the value of the variable MODULO, can be changed by means of the SHIFT SYMB view, or by using the VARS key. Many of the configurations addressed in the CFG menu are also referenced in these views. [. . . ]