Computer algebra system and titorial modes (30 pages)
Summary of Contents for Casio ALGEBRA FX
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ALGEBRA FX 2.0 PLUS FX 1.0 PLUS User’s Guide ( Additional Functions ) http://world.casio.com/edu_e/...
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CASIO ELECTRONICS CO., LTD. Unit 6, 1000 North Circular Road, London NW2 7JD, U.K. Important! Please keep your manual and all information handy for future reference.
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1-1-1 Advanced Statistics (STAT) 1-1 Advanced Statistics (STAT) u u u u u Function Menu The following shows the function menus for the STAT Mode list input screen. Pressing a function key that corresponds to the added item displays a menu that lets you select one of the functions listed below.
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1-1-2 Advanced Statistics (STAT) Σ MSE = – (a + b ln x • Logarithmic Regression ... n – 2 Σ MSE = (ln y – (ln a + bx • Exponential Repression ... n – 2 Σ MSE = •...
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1-1-3 Advanced Statistics (STAT) 4. After you are finished, press i to clear the coordinate values and the pointer from the display. · The pointer does not appear if the calculated coordinates are not within the display range. · The coordinates do not appear if [Off] is specified for the [Coord] item of the [SETUP] screen. ·...
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1-1-4 Advanced Statistics (STAT) u u u u u Common Functions • The symbol “ ■ ” appears in the upper right corner of the screen while execution of a calculation is being performed and while a graph is being drawn. Pressing A during this time terminates the ongoing calculation or draw operation (AC Break).
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1-2-1 Tests (TEST) 1-2 Tests (TEST) Test provides a variety of different standardization-based tests. They make it possible to test whether or not a sample accurately represents the population when the standard deviation of a population (such as the entire population of a country) is known from previous tests.
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1-2-2 Tests (TEST) The following pages explain various statistical calculation methods based on the principles described above. Details concerning statistical principles and terminology can be found in any standard statistics textbook. On the initial STAT Mode screen, press 3(TEST) to display the test menu, which contains the following items.
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1-2-3 Tests (TEST) Perform the following key operations from the statistical data list. 3(TEST) b(Z) b(1-Smpl) The following shows the meaning of each item in the case of list data specification. Data ......data type µ ........population mean value test conditions (“G µ ”...
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1-2-4 Tests (TEST) Calculation Result Output Example µ G11.4 ......direction of test ........score ........p-value ........mean of sample σ ......sample standard deviation (Displayed only for Data: List setting.) ........size of sample # [Save Res] does not save the µ condition in line 2.
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1-2-5 Tests (TEST) u u u u u 2-Sample Test This test is used when the standard deviations for two populations are known to test the hypothesis. The 2-Sample Test is applied to the normal distribution. – o : mean of sample 1 : mean of sample 2 σ...
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1-2-6 Tests (TEST) ......... mean of sample 1 ......... size (positive integer) of sample 1 ......... mean of sample 2 ......... size (positive integer) of sample 2 After setting all the parameters, align the cursor with [Execute] and then press one of the function keys shown below to perform the calculation or draw the graph.
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1-2-7 Tests (TEST) u u u u u 1-Prop Test This test is used to test for an unknown proportion of successes. The 1-Prop Test is applied to the normal distribution. : expected sample proportion – p : size of sample (1–...
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1-2-8 Tests (TEST) u u u u u 2-Prop Z Test This test is used to compare the proportion of successes. The 2-Prop Test is applied to the normal distribution. : data value of sample 1 – : data value of sample 2 : size of sample 1 p(1 –...
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1-2-9 Tests (TEST) > ......direction of test ........score ........p-value ˆ p ......... estimated proportion of sample 1 ˆ p ......... estimated proportion of sample 2 ˆ p ........estimated sample proportion ......... size of sample 1 ......... size of sample 2 # [Save Res] does not save the condition in line 2.
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1-2-10 Tests (TEST) k k k k k t Tests u u u u u t Test Common Functions You can use the following graph analysis functions after drawing a graph. • 1(T) ... Displays score. Pressing 1 (T) displays the score at the bottom of the display, and displays the pointer at the corresponding location in the graph (unless the location is off the graph screen).
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1-2-11 Tests (TEST) u u u u u 1-Sample t Test This test uses the hypothesis test for a single unknown population mean when the population standard deviation is unknown. The 1-Sample Test is applied to -distribution. µ o – : mean of sample σ...
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1-2-12 Tests (TEST) Calculation Result Output Example µ G 11.3 ...... direction of test ........score ........p-value ........mean of sample σ ......sample standard deviation ........size of sample # [Save Res] does not save the µ condition in line 2.
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1-2-13 Tests (TEST) u u u u u 2-Sample t Test 2-Sample Test compares the population means when the population standard deviations are unknown. The 2-Sample Test is applied to -distribution. The following applies when pooling is in effect. : mean of sample 1 –...
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1-2-14 Tests (TEST) The following shows the meaning of each item in the case of list data specification. Data ......data type µ ......... sample mean value test conditions (“G µ ” specifies two-tail test, “< µ ” specifies one-tail test where sample 1 is smaller than sample 2, “>...
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1-2-15 Tests (TEST) Calculation Result Output Example µ G µ ......direction of test ........score ........p-value ......... degrees of freedom ......... mean of sample 1 ......... mean of sample 2 σ ......standard deviation of sample 1 σ ......
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1-2-16 Tests (TEST) u u u u u LinearReg Test LinearReg Test treats paired-variable data sets as ( ) pairs, and uses the method of least squares to determine the most appropriate coefficients of the data for the regression formula .
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1-2-17 Tests (TEST) Calculation Result Output Example β G 0 & ρ G 0 ....direction of test ........score ........p-value ......... degrees of freedom ........constant term ........coefficient ........standard error ........correlation coefficient ......... coefficient of determination Pressing 6 (COPY) while a calculation result is on the display copies the regression formula to the graph formula editor.
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1-2-18 Tests (TEST) k k k k k χ Test χ Test sets up a number of independent groups and tests hypothesis related to the proportion of the sample included in each group. The χ Test is applied to dichotomous variables (variable with two possible values, such as yes/no).
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1-2-19 Tests (TEST) After setting all the parameters, align the cursor with [Execute] and then press one of the function keys shown below to perform the calculation or draw the graph. • 1(CALC) ... Performs the calculation. • 6(DRAW) ... Draws the graph. Calculation Result Output Example χ...
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1-2-20 Tests (TEST) k k k k k 2-Sample F Test 2-Sample Test tests the hypothesis for the ratio of sample variances. The Test is applied to the distribution. σ 1 n–1 σ 2 n–1 Perform the following key operations from the statistical data list. 3(TEST) e(F) The following is the meaning of each item in the case of list data specification.
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1-2-21 Tests (TEST) After setting all the parameters, align the cursor with [Execute] and then press one of the function keys shown below to perform the calculation or draw the graph. • 1(CALC) ... Performs the calculation. • 6(DRAW) ... Draws the graph. Calculation Result Output Example σ...
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1-2-22 Tests (TEST) k k k k k ANOVA ANOVA tests the hypothesis that the population means of the samples are equal when there are multiple samples. One-Way ANOVA is used when there is one independent variable and one dependent variable.
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1-2-23 Tests (TEST) Calculation Result Output Example One-Way ANOVA Line 1 (A) ....Factor A value, value, value, value, p-value Line 2 (ERR) ....Error value, value, value Two-Way ANOVA Line 1 (A) ....Factor A value, value, value, value, p-value Line 2 (B) ....
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1-2-24 Tests (TEST) k k k k k ANOVA (Two-Way) u u u u u Description The nearby table shows measurement results for a metal product produced by a heat treatment process based on two treatment levels: time (A) and temperature (B). The experiments were repeated twice each under identical conditions.
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1-2-25 Tests (TEST) u u u u u Input Example u u u u u Results 20010101...
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1-3-1 Confidence Interval (INTR) 1-3 Confidence Interval (INTR) A confidence interval is a range (interval) that includes a statistical value, usually the population mean. A confidence interval that is too broad makes it difficult to get an idea of where the population value (true value) is located.
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1-3-2 Confidence Interval (INTR) u u u u u General Confidence Interval Precautions Inputting a value in the range of 0 < C-Level < 1 for the C-Level setting sets you value you input. Inputting a value in the range of 1 < C-Level < 100 sets a value equivalent to your input divided by 100.
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1-3-3 Confidence Interval (INTR) k k k k k Z Interval u u u u u 1-Sample Z Interval 1-Sample Interval calculates the confidence interval for an unknown population mean when the population standard deviation is known. The following is the confidence interval. Left = o –...
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1-3-4 Confidence Interval (INTR) After setting all the parameters, align the cursor with [Execute] and then press the function key shown below to perform the calculation. • 1(CALC) ... Performs the calculation. Calculation Result Output Example Left ......interval lower limit (left edge) Right ......
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1-3-5 Confidence Interval (INTR) The following shows the meaning of each item in the case of list data specification. Data ......data type C-Level ......confidence level (0 < C-Level < 1) ......... population standard deviation of sample 1 ( >...
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1-3-6 Confidence Interval (INTR) u u u u u 1-Prop Z Interval 1-Prop Interval uses the number of data to calculate the confidence interval for an unknown proportion of successes. The following is the confidence interval. The value 100 (1 – ) % is the confidence level. : size of sample 1–...
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1-3-7 Confidence Interval (INTR) u u u u u 2-Prop Interval 2-Prop Z Interval uses the number of data items to calculate the confidence interval for the defference between the proportion of successes in two populations. The following is the confidence interval. The value 100 (1 – ) % is the confidence level. : size of sample 1–...
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1-3-8 Confidence Interval (INTR) Left ......interval lower limit (left edge) Right ......interval upper limit (right edge) ˆ p ......... estimated sample propotion for sample 1 ˆ p ......... estimated sample propotion for sample 2 ......... size of sample 1 .........
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1-3-9 Confidence Interval (INTR) ........mean of sample > 0) ......sample standard deviation ( ........size of sample (positive integer) After setting all the parameters, align the cursor with [Execute] and then press the function key shown below to perform the calculation. •...
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1-3-10 Confidence Interval (INTR) The following confidence interval applies when pooling is not in effect. The value 100 (1 – ) % is the confidence level. – o n–1 n–1 Left = (o )– t – o n–1 n–1 Right = (o )+ t df = (1–C)
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1-3-11 Confidence Interval (INTR) ......... mean of sample 1 > 0) of sample 1 ......standard deviation ( ......... size (positive integer) of sample 1 ......... mean of sample 2 > 0) of sample 2 ......standard deviation ( ......... size (positive integer) of sample 2 After setting all the parameters, align the cursor with [Execute] and then press the function key shown below to perform the calculation.
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1-4-1 Distribution (DIST) 1-4 Distribution (DIST) There is a variety of different types of distribution, but the most well-known is “normal distribution,” which is essential for performing statistical calculations. Normal distribution is a symmetrical distribution centered on the greatest occurrences of mean data (highest frequency), with the frequency decreasing as you move away from the center.
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1-4-2 Distribution (DIST) u u u u u Common Distribution Functions After drawing a graph, you can use the P-CAL function to calculate an estimated p-value for a particular x value. The following is the general procedure for using the P-CAL function. 1.
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1-4-3 Distribution (DIST) k k k k k Normal Distribution u u u u u Normal Probability Density Normal probability density calculates the probability density of nomal distribution from a specified value. Normal probability density is applied to standard normal distribution. (x –...
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1-4-4 Distribution (DIST) u u u u u Normal Distribution Probability Normal distribution probability calculates the probability of normal distribution data falling between two specific values. : lower boundary (x – ) – : upper boundary Perform the following key operations from the statistical data list. 5(DIST) b(Norm) c(C.D)
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1-4-5 Distribution (DIST) Calculation Result Output Example p ........normal distribution probability z:Low ......z:Low value (converted to standardize z score for lower value) z:Up ......z:Up value (converted to standardize z score for upper value) u u u u u Inverse Cumulative Normal Distribution Inverse cumulative normal distribution calculates a value that represents the location within a normal distribution for a specific cumulative probability.
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1-4-6 Distribution (DIST) After setting all the parameters, align the cursor with [Execute] and then press the function key shown below to perform the calculation. • 1(CALC) ... Performs the calculation. Calculation Result Output Examples x ........inverse cumulative normal distribution (Tail:Left upper boundary of integration interval) (Tail:Right lower boundary of integration interval) (Tail:Central upper and lower boundaries of integration...
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1-4-7 Distribution (DIST) k k k k k Student-t Distribution u u u u u Student-t Probability Density Student- probability density calculates probability density from a specified value. df+1 – df + 1 f (x) = Perform the following key operations from the statistical data list. 5(DIST) c(T) b(P.D)
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1-4-8 Distribution (DIST) u u u u u Student-t Distribution Probability Student- distribution probability calculates the probability of distribution data falling between two specific values. df + 1 : lower boundary df+1 – : upper boundary Perform the following key operations from the statistical data list. 5(DIST) c(T) c(C.D)
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1-4-9 Distribution (DIST) Calculation Result Output Example p ........Student- distribution probability t:Low ......t:Low value (input lower value) t:Up ......t:Up value (input upper value) k k k k k Distribution u u u u u Probability Density probability density calculates the probability density function for the distribution at a specified value.
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1-4-10 Distribution (DIST) Calculation Result Output Example p ........probability density when the [Stat Wind] setting is [Auto]. # Current V-Window settings are used for graph drawing when the SET UP screen's Xmin = 0, Xmax = 11.5, Xscale = 2, [Stat Wind] setting is [Manual].
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1-4-11 Distribution (DIST) u u u u u Distribution Probability distribution probability calculates the probability of distribution data falling between two specific values. : lower boundary –1 – : upper boundary Perform the following key operations from the statistical data list. 5(DIST) c(C.D) Data is specified using parameter specification.
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1-4-12 Distribution (DIST) Calculation Result Output Example p ........distribution probability k k k k k F Distribution u u u u u F Probability Density probability density calculates the probability density function for the F distribution at a specified value.
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1-4-13 Distribution (DIST) Calculation Result Output Example p ........F probability density # V-Window settings for graph drawing are set Window settings are used for graph drawing automatically when the SET UP screen's when the [Stat Wind] setting is [Manual]. [Stat Wind] setting is [Auto].
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1-4-14 Distribution (DIST) u u u u u F Distribution Probability distribution probability calculates the probability of distribution data falling between two specific values. : lower boundary n + d n + d : upper boundary – –1 Perform the following key operations from the statistical data list. 5(DIST) e(F) c(C.D)
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1-4-15 Distribution (DIST) Calculation Result Output Example p ........F distribution probability 20010101...
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1-4-16 Distribution (DIST) k k k k k Binomial Distribution u u u u u Binomial Probability Binomial probability calculates a probability at a specified value for the discrete binomial distribution with the specified number of trials and probability of success on each trial. n –...
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1-4-17 Distribution (DIST) Calculation Result Output Example p ........binomial probability u u u u u Binomial Cumulative Density Binomial cumulative density calculates a cumulative probability at a specified value for the discrete binomial distribution with the specified number of trials and probability of success on each trial.
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1-4-18 Distribution (DIST) After setting all the parameters, align the cursor with [Execute] and then press the function key shown below to perform the calculation. • 1(CALC) ... Performs the calculation. Calculation Result Output Example p ......... probability of success 20010101 20011101...
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1-4-19 Distribution (DIST) k k k k k Poisson Distribution u u u u u Poisson Probability Poisson probability calculates a probability at a specified value for the discrete Poisson distribution with the specified mean. – f (x) = = 0, 1, 2, ···) : mean ( >...
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1-4-20 Distribution (DIST) u u u u u Poisson Cumulative Density Poisson cumulative density calculates a cumulative probability at specified value for the discrete Poisson distribution with the specified mean. Perform the following key operations from the statistical data list. 5(DIST) g(Poissn) c(C.D)
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1-4-21 Distribution (DIST) k k k k k Geometric Distribution u u u u u Geometric Probability Geometric probability calculates the probability at a specified value, and the number of the trial on which the first success occurs, for the geometric distribution with a specified probability of success.
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1-4-22 Distribution (DIST) u u u u u Geometric Cumulative Density Geometric cumulative density calculates a cumulative probability at specified value, the number of the trial on which the first success occurs, for the discrete geometric distribution with the specified probability of success. Perform the following key operations from the statistical data list.