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Casio STAT 2 Manual

Casio STAT 2 Manual

Statistical calculation (stat) software for the algebra fx2.0
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STAT 2
(Advanced Statistics Application)
Statistical Calculation (STAT) Soft-
ware for the ALGEBRA FX2.0
1. Modifications Made to ALGEBRA 2.0 by STAT2
2. Tests
3. Confidence Interval
4. Distribution

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Summary of Contents for Casio STAT 2

  • Page 1 STAT 2 (Advanced Statistics Application) Statistical Calculation (STAT) Soft- ware for the ALGEBRA FX2.0 1. Modifications Made to ALGEBRA 2.0 by STAT2 2. Tests 3. Confidence Interval 4. Distribution...
  • Page 2 1.Modifications Made to ALGEBRA 2.0 by STAT2 u u u u u Changes to the Function Menu Installing STAT2 changes the function menu of the STAT Mode list input screen (initial screen) as shown below. Pressing a function key that corresponds to the added item displays a menu that lets you select one of the functions listed below.
  • Page 3 MSE = (ln y – (ln a + bx • Exponential Repression ... n – 2 MSE = (ln y – (ln a + b ln x • Power Regression ... n – 2 i =1 MSE = – (a sin (bx + c) + d )) •...
  • Page 4 · The coordinates do not appear if [Off] is specified for the [Coord] item of the [SETUP] screen. · The Y-CAL function can also be used with a graph drawn by using DefG feature. u u u u u Regression Formula Copy Function from a Regression Calculation Result Screen In addition to the existing regression formula copy function that lets you copy the regression calculation result screen after drawing a statistical graph (such as Scatter Plot), STAT2 also...
  • Page 5 · Pressing A while a calculation result is on the display returns to the parameter setting screen. • Pressing u 5 (G"T) after drawing a graph switches to the parameter setting screen (G"T function). Pressing u 5 (G"T) again returns to the graph screen. ·...
  • Page 6 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.
  • Page 7 On the initial STAT2 Mode screen, press 3 (TEST) to display the test menu, which contains the following items. • 3(TEST)b(Z) ... Tests (p.7) c(T) ... Tests (p.15) ) ... ! Test (p.23) e(F) ... 2-Sample Test (p.25) f(ANOVA) ... ANOVA (p.27) k k k k k Tests u u u u u...
  • Page 8 Perform the following key operation 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 ”...
  • Page 9 • 1(CALC) ... Performs the calculation. • 6(DRAW) ... Draws the graph. Calculation Result Output Example µ G11.4 ......direction of test ........score ........p-value ........mean of sample ......sample standard deviation " (Displayed only for Data: List setting) ........
  • Page 10 u u u u u 2-Sample Test This test is used when the sample standard deviations for two populations are known to test the hypothesis. The 2-Sample Test is applied to normal distribution. – o : mean of sample 1 : mean of sample 2 "...
  • Page 11 ......... 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.
  • Page 12 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 normal distribution. : expected sample proportion – p : size of sample (1– p Perform the following key operation from the statistical data list. 3(TEST) b(Z) d(1-Prop)
  • Page 13 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 normal distribution. : data value of sample 1 – : data value of sample 2 : size of sample 1 p(1 –...
  • Page 14 > ......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.
  • Page 15 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).
  • Page 16 u u u u u 1-Sample t Test This test uses the hypothesis test for a single unknown population mean when the popula- tion standard deviation is unknown. The 1-Sample Test is applied to t-distribution. o – µ : mean of sample "...
  • Page 17 Calculation Result Output Example µ G 11.3 ...... direction of test ........score ........p-value ........mean of sample ......Sample standard deviation " ........size of sample # [Save Res] does not save the µ condition in line 2.
  • Page 18 u u u u u 2-Sample t Test 2-Sample Test compares the population means when standard deviations are unknown. The 2-Sample Test is applied to t-distribution. – o : mean of sample 1 : mean of sample 2 " " 1 n –1 2 n –1 : standard deviation of sample 1...
  • Page 19 The following shows the meaning of each item in the case of list data specification. Data ......data type ......... sample mean value test conditions (“G µ ” specifies two-tail µ test, “< µ ” specifies one-tail test where sample 1 is smaller than sample 2, “>...
  • Page 20 ........p-value ......... degrees of freedom ......... mean of sample 1 ......... mean of sample 2 ......standard deviation of sample 1 " ......standard deviation of sample 2 " ......pooled sample standard deviation (Displayed only when " Pooled: On Setting.) .........
  • Page 21 u u u u u LinearReg Test LinearReg Test treats paired-variable data sets as ( ) pairs and plots all data on a graph. Next, a straight line ( ) is drawn through the area where the greatest number of plots are located and the degree to which a relationship exists is calculated. : intercept ( x –...
  • Page 22 Calculation Result Output Example $ G 0 & % 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.
  • Page 23 k k k k k ! Test Test sets up a number of independent groups and tests hypothesis related to the proportion of the sample included in each group. The ! Test is applied to dichotomous variables (variable with two possible values, such as yes/no). expected counts : all data values &...
  • Page 24 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 .........
  • Page 25 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 distribution. " 1 n–1 " 2 n–1 Perform the following key operation from the statistical data list. 3(TEST) e(F) The following is the meaning of each item in the case of list data specification.
  • Page 26 Calculation Result Output Example G " ......direction of test " ........value ........p-value ......... mean of sample 1 (Displayed only for Data: List Setting) ......... mean of sample 2 (Displayed only for Data: List Setting) ......standard deviation of sample 1 "...
  • Page 27 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. Two-Way ANOVA is used when there here are two independent variables and one depend- ent variable.
  • Page 28 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) ....Factor B value, value, value,...
  • Page 29 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.
  • Page 30 u u u u u Input Example u u u u u Results...
  • Page 31 3. Confidence Interval (INTR) A confidence interval is a range (interval) that includes the population mean value. A confidence interval that is too broad makes it difficult to get an idea of where the population value (true value) is located. A narrow confidence interval, on the other hand, limits the population value and makes it possible to obtain reliable results.
  • Page 32 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.
  • Page 33 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 standard deviation is known. The following is the confidence interval. Left = o – Z ! "...
  • Page 34 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 ......interval upper limit (right edge) ........
  • Page 35 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 ( " > 0) " .........
  • Page 36 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 –...
  • Page 37 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.
  • Page 38 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 ......... size of sample 2 k k k k k t Interval u u u u u 1-Sample t Interval 1-Sample...
  • Page 39 ........mean of sample ......sample standard deviation ( > 0) " " ........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. •...
  • Page 40 The following confidence interval applies when pooling is not in effect. The value 100 (1- % is the confidence level. " " n–1 Left = (o – o )– t n–1 " " Right = (o – o )+ t n–1 n–1 df =...
  • Page 41 ......... mean of sample 1 ......standard deviation ( > 0) of sample 1 " " ......... 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.
  • Page 42 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.
  • Page 43 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. After drawing a graph, press 1 (P-CAL) to display the x value input dialog box. 2.
  • Page 44 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 that data taken from a specified value. Normal probability density is applied to standard normal distribution.
  • Page 45 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 – µ) µ – : upper boundary "# Perform the following key operation from the statistical data list. (DIST) (Norm) (C.D)
  • Page 46 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.
  • Page 47 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 interval)
  • Page 48 k k k k k Student-t Distribution u u u u u Student-t Probability Density Student- probability density calculates the probability density of distribution that data taken from a specified x value. df+1 – df + 1 f (x) = "...
  • Page 49 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 operation from the statistical data list. 5(DIST) c(T) c(C.D)
  • Page 50 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 probabilitty density function for the ! distribution at a specified value.
  • Page 51 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, Ymin = -0.1, [Stat Wind] setting is [Manual].
  • Page 52 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 operation from the statistical data list. 5(DIST) c(C.D) Data is specified using parameter specification.
  • Page 53 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. n + d n + d –...
  • Page 54 Calculation Result Output Example p ... 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]. Current V-...
  • Page 55 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 operation from the statistical data list. 5 (DIST) e (F) c (C.D)
  • Page 56 Calculation Result Output Example p ... distribution probability...
  • Page 57 k k k k k Binomial Distribution u u u u u Binomial Probability Binomial probability calculates a probability at specified value for the discrete binomial distribution with the specified numtrials and probability of success on each trial. n) p = 0, 1, ·······, : success probability n –...
  • Page 58 Calculation Result Output Example p ... Binomial probability u u u u u Binomial Cumulative Density Binomial cumulative density calculates a cumulative probability at specified value for the discrete binomial distribution with the specified numtrials and probability of success on each trial.
  • Page 59 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 ... Binomial cumulative density...
  • Page 60 k k k k k Poisson Distribution u u u u u Poisson Probability Poisson probability calculates a probability at specified value for the discrete Poisson distribu- tion with the specified mean. – µ µ f (x) = = 0, 1, 2, ···) µ...
  • Page 61 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 operation from the statistical data list. 5 (DIST) g (Poissn) c (C.D) The following shows the meaning of each item when data is specified using list specification.
  • Page 62 k k k k k Geometric Distribution u u u u u Geometric Probability Geometric probability calculates a 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.
  • Page 63 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 operation from the statistical data list.
  • Page 64 Examples...
  • Page 65 examples k k k k k 1-Sample Test Set Up 1. On the icon menu, select STAT2. Execution 2. When using list data (List is selected as the Data parameter), be sure to input data into the list first. 3. 3(TEST)b(Z)b(1-Smpl) ... 1-Sample Test 4.

  • Page 66: Result Screen

    examples Example Five new members of a football team are timed for the 100- meter dash, yielding the following times. A: 12.5 B: 11.6 C: 10.8 D: 12.8 E: 11.4 The average time of current team members is 11.4 seconds, with a standard deviation of 1.30.
  • Page 67 examples k k k k k 2-Sample Test Set Up 1. On the icon menu, select STAT2. Execution 2. When using list data (List is selected as the Data parameter) , be sure to input data into the list first. 3.
  • Page 68 examples Example A consumer group is testing camp stoves. To test the heating capacity of a stove they measure the time required to bring 2 qt of water from 50 q q q q q F to boiling (at sea level). Two competing models are under consideration.
  • Page 69 examples k k k k k 1-Prop Test Set Up 1. On the icon menu, select STAT2. Execution 2. 3(TEST)b(Z)d(1-Prop) ... 1-Prop Test 3. Set calculation parameters. 4. Align the cursor with [Execute] 1(CALC) ... Performs calculation. 6(DRAW) ... Draws graph.
  • Page 70 examples Example A team of eye surgeons has developed a new technique for a risky eye operation to restore the sight of people blinded from a certain disease. Under the old method it is known that only 30% of the patients who undergo this operation recover their eyesight.
  • Page 71 examples k k k k k 2-Prop Test Set Up 1. On the icon menu, select STAT2. Execution 2. 3(TEST)b(Z)e(2-Prop) ... 2-Prop Test 3. Set calculation parameters. 4. Align the cursor with [Execute] 1(CALC) ... Performs calculation. 6(DRAW) ... Draws graph.
  • Page 72 examples Example The County Clerk wishes to improve voter registration. One method under consideration is to send reminders in the mail to all citizens in the county who are eligible to register. As a pilot study to determine if this method will actually improve voter registration, a random sample of 1224 potential voters was taken.
  • Page 73 examples k k k k k 1-Sample Test Set Up 1. On the icon menu, select STAT2. Execution 2. When using list data (List is selected as the Data parameter), be sure to input data into the list first. 3. 3(TEST)c(T)b(1-Smpl) ... 1-Sample Test 4.
  • Page 74 examples Example A company manufactures large rocket engines used to project satellites into space. The government buys the rockets, and the contract specifies that these engines are to use an average of 5550 lb of rocket fuel the first 15 sec operation. The company claims their engines fit specifications.
  • Page 75 examples k k k k k 2-Sample Test (Pooled On) Set Up 1. On the icon menu, select STAT2. Execution 2. When using list data (List is selected as the Data parameter), be sure to input data into the list first. 3.
  • Page 76 examples Example Two different processes (Type A and Type B) are used to produce tinplate. The following values show the weights of samples produced by each process. Type A: 105 108 86 103 103 107 124 124 Type B: 97 103 107 Using the level of significance 0.05, test the null hypothesis that the tinplate produced by the two processes are of the same level.
  • Page 77 examples k k k k k 2-Sample Test (Pooled Off) Set Up 1. On the icon menu, select STAT2. Execution 2. When using list data (List is selected as the Data parameter) , be sure to input data into the list first. 3.
  • Page 78 examples Example Two competing headache remedies claim to give fast-acting relief. An experiment was performed to compare the mean lengths of time required for bodily absorption of brand A and brand B headache remedies. 12 people were randomly selected and given an oral dosage of brand A.
  • Page 79 examples k k k k k LinearReg Test Set Up 1. On the icon menu, select STAT2. Execution 2. Input data into the list. 3. 3(TEST)c(T)d(LinReg) ... LinearReg Test 4. Set calculation parameters. 5. Align the cursor with [Execute] 1(CALC) ... Performs calculation.
  • Page 80 examples Example A survey conducted by a city on its real estate investments revealed the following data on the relationship between area and price. Does the data indicate that the value # , that is, the slope of the popula- tion regression line, is not zero, which would mean that (Area) can be use as a predictor of y (Sales Price)? Use a 5% level of significance.
  • Page 81 examples k k k k k & Test Set Up 1. On the icon menu, select STAT2. Execution 2. 3(TEST)d( & )... & Test 3. Input data into the Matrix. 4. Set calculation parameters. 5. Align the cursor with [Execute] 1(CALC) ...
  • Page 82 examples Example A certain club collected data on the attendance at meetings by married status, and obtained the data shown below. Married Divorced Widowed Single Row Totals Often Absent Seldom Absent Never Absent Column Totals Test the null hypothesis that two phenomena are independent using the level of significance of 0.05.
  • Page 83 examples k k k k k 2-Sample Test Set Up 1. On the icon menu, select STAT2. Execution 2. When using list data (List is selected as the Data parameter), be sure to input data into the list first. 3. 3(TEST)e(F)... 2-Sample F Test 4.
  • Page 84 examples Example There are two possible routes to get to the airport from a certain company, and so manager wants to determine which route is the fastest in order to make a plane that leaves at 7 o'clock. One route was researched five times and then the other route was researched five times, producing the data shown below.
  • Page 85 examples k k k k k One-Way ANOVA Set Up 1. On the icon menu, select STAT2. Execution 2. Input data into the list. 3. 3(TEST)f(ANOVA) ... Analysis of Variance (ANOVA) 4. Set calculation parameters. Specify 1 for How Many setting. 5.
  • Page 86 examples Example A psychologist is studying pattern recognition skills under four laboratory settings. In each setting, a fourth-grade child is given a pattern recognition test with ten patterns to identify. In setting A, the child is given praise for each correct answer and no comment about wrong answers.
  • Page 87 examples k k k k k Two-Way ANOVA Set Up 1. On the icon menu, select STAT2. Execution 2. Input data into the list. 3. 3(TEST)f(ANOVA) ... Analysis of Variance (ANOVA) 4. Set calculation parameters. Specify 2 for How Many setting. 5.
  • Page 88 examples Procedure 1 m STAT2 2 bwbwbwbwcwcwcwcwe bwbwcwcwbwbwcwcwe bbdwbbgwbdjwbdcwbddwbd bwbcgwbccw 3 3(TEST) f(ANOVA) 4 2(2)c 1(LIST) bwc 1(LIST) cwc 1(LIST) dwc 1(None) c 5 1(CALC) 6(DRAW) Result Screen • Time differential (A) : Since P=0.2458019517 > 0.05 (level of significance), we can not reject the null hypothesis. •...
  • Page 89 examples k k k k k 1-Sample Z Interval Set Up 1. On the icon menu, select STAT2. Execution 2. When using list data (List is selected as the Data parameter), be sure to input data into the list first. 3.
  • Page 90 examples Example In a random sample of size n = 20 from a normal population with the standard deviation ! = 15 and the mean o o o o o = 64.3, construct a 95% confidence interval for the population mean µ . Procedure 1 m STAT2 2 4(INTR) b(Z)b(1-Smpl)
  • Page 91 examples k k k k k 2-Sample Z Interval Set Up 1. On the icon menu, select STAT2. Execution 2. When using list data (List is selected as Data parameter), be sure to input data into the list first. 3. 4(INTR)b(Z)c(2-Smpl)... 2-Sample Z Interval 4.
  • Page 92 examples Example Construct a 94% confidence interval for the difference between the mean lifetimes of two kinds of light bulbs( µ - µ ), given that random sample of 40 light bulbs of the first kind lasted on the average for 418 hours of continuous use and 50 light bulbs of the second kind lasted on the average for 402 hours of continuous use.
  • Page 93 examples k k k k k 1-Prop Z Interval Set Up 1. On the icon menu, select STAT2. Execution 2. 4(INTR)b(Z)d(1-Prop)... 1-Prop Z Interval 3. Set calculation parameters. 4. Align the cursor with [Execute] 1(CALC) ... Performs calculation.
  • Page 94 examples Example Suppose 800 students were selected at random from a student body of 20,000 and given shots to prevent a certain type of flu. All 800 students were exposed to the flu and 600 of them did not get the flu. Let p present the probability that the shot will be successful for any single student selected at random from the entire population of 20,000.
  • Page 95 examples k k k k k 2-Prop Z Interval Set Up 1. On the icon menu, select STAT2. Execution 2. 4(INTR)b(Z)e(2-Prop)... 2-Prop Z Interval 3. Set calculation parameters. 4. Align the cursor with [Execute] 1(CALC) ... Performs calculation.
  • Page 96 examples Example If 132 of 200 male voters and 90 of 150 female voters favor a certain candidate running for governor of Texas, find a 99% confidence interval for the difference between the actual proportions of male and female voters who favor the candidate. Procedure 1 m STAT2 2 4(INTR) b(Z)e(2-Prop)
  • Page 97 examples k k k k k 1-Sample t Interval Set Up 1. On the icon menu, select STAT2. Execution 2. When using list data (List is selected as Data parameter), be sure to input data into the list first. 3. 4(INTR)c(T)b(1-Smpl)... 1-Sample t Interval 4.
  • Page 98 examples Example A paint manufacture wants to determine the average drying time of a new interior wall paint. If for 12 test areas of equal size he obtained a mean drying time of 66.3 minutes and a standard deviation of 8.4 minutes, construct a 95% confidence interval for the population mean µ...
  • Page 99 examples k k k k k 2-Sample t Interval (Pooled On) Set Up 1. On the icon menu, select STAT2. Execution 2. When using list data (List is selected as the Data parameter), be sure to input data into the list first. 3.
  • Page 100 examples Example Factory A and Factory B both manufacture the same item. To compare the productivity of the two factories, the production data shown below was collected for 10 items at Factory A and nine items at Factory B. Factory A: 78, 80, 79, 83, 82, 85, 78, 74, 76, 84 (kg/h) Factory B: 81, 84, 82, 88, 86, 83, 78, 84, 89 (kg/h) Construct a 95% confidence interval for the difference between µ...
  • Page 101 examples k k k k k 2-Sample t Interval (Pooled Off) Set Up 1. On the icon menu, select STAT2. Execution 2. When using list data (List is selected as the Data parameter), be sure to input data into the list first. 3.
  • Page 102 examples Example Factory A and Factory B both manufacture the same item. To compare the productivity of the two factories, the production data shown below was collected for 10 items at Factory A and nine items at Factory B. Factory A: 78, 80, 79, 83, 82, 85, 78, 74, 76, 84 (kg/h) Factory B: 81, 84, 82, 88, 86, 83, 78, 84, 89 (kg/h) Construct a 95% confidence interval for the difference between µ...
  • Page 103 examples k k k k k Normal Probability Density Set Up 1. On the icon menu, select STAT2. Execution 2. 5(DIST)b(Norm)b(P.D)... Normal Probability Density 3. Set calculation parameters. 4. Align the cursor with [Execute] 1(CALC) ... Performs calculation. 6(DRAW) ... Draws graph.
  • Page 104 examples Example Calculate probability density p when the random variable for normal distribution N (35, 2 ) is 36. Procedure 1 m STAT2 2 5(DIST) b(Norm)b(P.D) 3 dgw 1(None)c 4 1(CALC) Result Screen Result: p = 0.176 6(DRAW) (Pressing6(DRAW) draws the graph.) 6 1(P-CAL) Enter the X-coordinate.
  • Page 105 examples k k k k k Normal Distribution Probability Set Up 1. On the icon menu, select STAT2. Execution 2. 5(DIST)b(Norm)c(C.D)... Normal Distribution Probability 3. Set calculation parameters. 4. Align the cursor with [Execute] 1(CALC) ... Performs calculation.
  • Page 106 examples Example Given that x is normal distribution with µ = –25 and ! = 4, find Pr (–21 < < < < < x < < < < < –19). Procedure 1 m STAT2 2 5(DIST)b(Norm)c(C.D) 3 -cbw -bjw -cfw 1(None)c 4 1(CALC)
  • Page 107 examples k k k k k Inverse Cumulative Normal Distribution Set Up 1. On the icon menu, select STAT2. Execution 2. 5(DIST)b(Norm)d(Invrse)... Inverse Cumulative Normal Distribution 3. Set calculation parameters. 4. Align the cursor with [Execute] 1(CALC) ... Performs calculation.
  • Page 108 examples Example Find z so that 5% of the area under the standard normal distribution curve lies to the right of z. Procedure 1 m STAT2 2 5(DIST)b(Norm)d(Invrse) 3 2(RIGHT)c .afw 1(None)c 4 1(CALC) Result Screen Result: = 1.645...
  • Page 109 examples k k k k k Student-t Probability Density Set Up 1. On the icon menu, select STAT2. Execution 2. 5(DIST)c(T)b(P.D)... Student-t Probability Density 3. Set calculation parameters. 4. Align the cursor with [Execute] 1(CALC) ... Performs calculation. 6 (DRAW) ... Draws graph.
  • Page 110 examples Example Calculate probability density p when random variable x is 1 for a t- distribution with degrees of freedom is 2. Procedure 1 m STAT2 2 5(DIST)c(T)b(P.D) 3 bw 1(None)c 4 1(CALC) Result Screen Result: p = 0.192 6(DRAW) (Pressing 6(DRAW) draws the graph.) 6 1(P-CAL)
  • Page 111 examples k k k k k Student-t Distribution Probability Set Up 1. On the icon menu, select STAT2. Execution 2. 5(DIST)c(T)c(C.D)... Student-t Distribution Probability 3. Set calculation parameters. 4. Align the cursor with [Execute] 1(CALC) ... Performs calculation.
  • Page 112 examples Example Find point t when the right side probability is 0.05 for a -distribution with degrees of freedom is 15. Procedure 1 m STAT2 2 5(DIST)c(T)c(C.D) 3 b.hw bEjjw 1(None)c 4 1(CALC) 1.7 < ffffb.iw 1(CALC) 1.7 < < 1.8 ffffb.hfw 1(CALC) 1.75 <...
  • Page 113 examples k k k k k ! Probability Density Set Up 1. On the icon menu, select STAT2. Execution 2. 5(DIST)d(! )b(P.D)... ! Probability Density 3. Set calculation parameters. 4. Align the cursor with [Execute] 1(CALC) ... Performs calculation. 6(DRAW) ... Draws graph.
  • Page 114 examples Example Calculate probability density p when random variable x is 1 for a ! distribution with degrees of freedom is 3. Procedure 1 m STAT2 2 5(DIST)d(! )b(P.D) 3 bw 1(None)c 4 1(CALC) Result Screen Result: p = 0.242 6(DRAW) (Pressing 6(DRAW) draws the graph.)
  • Page 115 examples k k k k k ! Distribution Probability Set Up 1. On the icon menu, select STAT2. Execution 2. 5(DIST)d(! )c(C.D)... ! Distribution Probability 3. Set calculation parameters. 4. Align the cursor with [Execute] 1(CALC) ... Performs calculation.
  • Page 116 examples Example Calculate the probability of a ! distribution when the degrees of freedom is 4 and the upper limit is ! = 2. Procedure 1 m STAT2 2 5(DIST)d(! )c(C.D) 3 aw 1(None)c 4 1(CALC) Result Screen Result : p = 0.264...
  • Page 117 examples k k k k k F Probability Density Set Up 1. On the icon menu, select STAT2. Execution 2. 5(DIST)e(F)b(P.D)... F Probability Density 3. Set calculation parameters. 4. Align the cursor with [Execute] 1(CALC) ... Performs calculation. 6(DRAW) ... Draws graph.
  • Page 118 examples Example Calculate probability density p when random variable x is 1 for an F- distribution with numerator degrees of freedem is 24 and denominator degrees of freedom is 19. Procedure 1 m STAT2 2 5(DIST)e(F)b(P.D) 3 bw 1(None)c 4 1(CALC) Result Screen Result: p = 0.908 6(DRAW)
  • Page 119 examples k k k k k F Distribution Probability Set Up 1. On the icon menu, select STAT2. Execution 2. 5(DIST)e(F)c(C.D)... F Distribution Probability 3. Set calculation parameters. 4. Align the cursor with [Execute] 1(CALC) ... Performs calculation.
  • Page 120 examples Example Calculate the probability of F distribution when the lower limit is 0, the upper limit is 1.9824, n:df = 19, and d:df = 16. Procedure 1 m STAT2 2 5(DIST)e(F)c(C.D) 3 aw b.jicew 1(None)c 4 1(CALC) Result Screen Result : p = 0.914...
  • Page 121 examples k k k k k Binomial Probability Set Up 1. On the icon menu, select STAT2. Execution 2. When using list data (List is selected as the Data parameter) , be sure to input data into the list first. 3.
  • Page 122 examples Example 20 white marbles and 30 red marbles are placed into a container. One marble is taken out of and then replaced into the container, and then another marble is removed. Calculate the probability of a white marble being picked 0, 1, and 2 times. Procedure 1 m STAT2 2 5(DIST)f(Binmal)b(P.D)
  • Page 123 examples k k k k k Binomial Cumulative Density Set Up 1. On the icon menu, select STAT2. Execution 2. When using list data (List is selected as the Data parameter) , be sure to input data into the list first. 3.
  • Page 124 examples Example George is taking a multiple-choice examination that consists of five questions . Each question has four possible answers. George guesses at every answer. What is the probability that he can only answer three questions or less? Procedure 1 m STAT2 2 5(DIST)f(Binmal)c(C.D) 3 2(VAR)c .cfw...
  • Page 125 examples k k k k k Poisson Probability Set Up 1. On the icon menu, select STAT2. Execution 2. When using list data (List is selected as the Data parameter) , be sure to input data into the list first. 3.
  • Page 126 examples Example The probability of scratches occurring in the wire during a certain wire drawing process is 0.1 per meter. This means that you can expect 1.5 scratches for every 15 meters of wire. Calculate the possibilities of 0, 1, and 2 scratches occurring. Procedure 1 m STAT2 2 aw...
  • Page 127 examples k k k k k Poisson Cumulative Density Set Up 1. On the icon menu, select STAT2. Execution 2. When using list data (List is selected as the Data parameter) , be sure to input data into the list first. 3.

  • Page 128: Result Screen

    examples Example The average number of trucks arriving on any one day at a truck depot in a certain city is known to be 12. What is a probability that on a given day fewer than 9 trucks will arrive at this depot? Procedure 1 m STAT2 2 5(DIST)g(Poissn)c(C.D)
  • Page 129 examples k k k k k Geometric Probability Set Up 1. On the icon menu, select STAT2. Execution 2. When using list data (List is selected as the Data parameter) , be sure to input data into the list first. 3.
  • Page 130 examples Example If the probability is 75% that an applicant for a driver's licence will pass the road test on any given try. What is the probability that an applicant will finally pass the test on the 4th try? Procedure 1 m STAT2 2 5(DIST)h(Geo)b(P.D) 3 2(VAR)c...
  • Page 131 examples k k k k k Geometric Cumulative Density Set Up 1. On the icon menu, select STAT2. Execution 2. When using list data (List is selected as the Data parameter) , be sure to input data into the list first. 3.
  • Page 132 examples Example Calculate the geometric cumulative probability for x = 2, 3, 4 when p = 0.5. Procedure 1 m STAT2 2 5(DIST)h(Geo)c(C.D) 3 2(VAR)c 1(None)c 4 1(CALC) 1(CALC) 1(CALC) Result Screen Results: p = 0.75 when = 2; p = 0.875 when = 3;...